A month before the 2020 election, Joseph R. Biden Jr.’s daughter, Ashley, received a call from a man offering help. Striking a friendly tone, the man said that he had found a diary that he believed belonged to Ms. Biden and that he wanted to return it to her.

Ms. Biden had in fact kept a diary the previous year as she recovered from addiction and had stored it and some other belongings at a friend’s home in Florida where she had been living until a few months earlier. The diary’s highly personal contents, if publicly disclosed, could prove an embarrassment or a distraction to her father at a critical moment in the campaign.

She agreed with the caller to send someone to retrieve the diary the next day.

But Ms. Biden was not dealing with a good Samaritan.

The man on the other end of the phone worked for Project Veritas, a conservative group that had become a favorite of President Donald J. Trump, according to interviews with people familiar with the sequence of events. From a conference room at the group’s headquarters in Westchester County, N.Y., surrounded by other top members of the group, the caller was seeking to trick Ms. Biden into confirming the authenticity of the diary, which Project Veritas was about to purchase from two intermediaries for $40,000.

The caller did not identify himself as being affiliated with Project Veritas, according to accounts from two people with knowledge of the conversation. By the end of the call, several of the group’s operatives who had either listened in, heard recordings of the call or been told of it believed that Ms. Biden had said more than enough to confirm that it was hers.

The new details of Project Veritas’s effort to establish that the diary was Ms. Biden’s are elements of a still-emerging story about how Trump supporters and a group known for its undercover sting operations worked to expose personal information about the Biden family at a crucial stage of the 2020 campaign.

Drawn from interviews, court filings and other documents, the new information adds further texture to what is known about an episode that has led to a criminal investigation of Project Veritas by federal prosecutors who have suggested they have evidence that the group was complicit in stealing Ms. Biden’s property and in transporting stolen goods across state lines.

And by showing that Project Veritas employed deception rather than traditional journalistic techniques in the way it approached Ms. Biden — the caller identified himself with a fake name — the new accounts could further complicate the organization’s assertions in court filings that it should be treated as a publisher and granted First Amendment protections. Project Veritas regularly carries out undercover stings, surveillance operations and ambush interviews, mostly against liberal groups and journalists.

At the same time, new information about the case suggests that the effort to make the diary public reached deeper into Mr. Trump’s circle than previously known.

A month before the call to Ms. Biden, the diary had been passed around a Trump fund-raiser in Florida at the home of a donor who helped steer the diary to Project Veritas and was later nominated by Mr. Trump to the National Cancer Advisory Board. Among those attending the event was Donald Trump Jr., though it is not clear if he examined it.

Federal prosecutors have been investigating how Project Veritas obtained the diary, and last fall carried out searches at the homes of three of the group’s operatives, including that of its founder, James O’Keefe. In court filings, prosecutors have suggested that the organization was complicit in the theft of some of Ms. Biden’s other belongings, which interviews show the group obtained as it was seeking to confirm the diary’s authenticity.

Project Veritas — which is suing The New York Times for defamation in an unrelated case — has denied any wrongdoing or knowledge that the belongings had been stolen. It has portrayed itself as a media organization that is being unfairly investigated for simply doing journalism and has assailed the Justice Department and the F.B.I. for their handling of the case.

Prosecutors have signaled that they view the circumstances very differently, all but dismissing in one court filing the group’s defense that it was acting as a news organization, saying that “there is no First Amendment protection for the theft and interstate transport of stolen property.”

In response to a request to Project Veritas for comment, Mr. O’Keefe sent an email criticizing The Times. “Imagine writing so thoroughly divergent from reality and so mendacious with innuendo that there is literally no utterance that won’t make it worse,” he said.

Spokesmen for the F.B.I. and for federal prosecutors overseeing the case in the Southern District of New York declined to comment, as did Roberta Kaplan, a lawyer for Ms. Biden.

The Times has previously reported that the story of Project Veritas’s involvement with the diary began in the months leading up to Election Day.

In July 2020, a single mother of two moved into the rented home of a former boyfriend in Delray Beach, Fla. The woman, Aimee Harris, a Trump supporter, told the former boyfriend that she had little money, had nowhere to live and was in a bitter custody dispute. Shortly after moving into the rental, Ms. Harris learned that Ms. Biden — also a friend of the former boyfriend — had been staying at the home earlier that year during the pandemic.

Ms. Biden had moved back to the Philadelphia area in June 2020, around the time her father clinched the Democratic Party’s nomination for president. She stored a couple of bags of her belongings at the rental house along with her diary, and she told her friend, who was leasing the home, that she planned to return to retrieve her things in the fall.

In August, Ms. Harris reached out to Robert Kurlander, a friend who had been sentenced to 40 months in prison in the 1990s on a federal fraud charge and had expressed anti-Biden sentiments online, to say she had found the diary. The two believed they could sell it, allowing Ms. Harris to help pay for the lawyers representing her in the custody dispute.

New details from interviews and documents have further fleshed out what happened next. Mr. Kurlander contacted Elizabeth Fago, the Trump donor who would host the fund-raiser attended by Donald Trump Jr. When first told of the diary, Ms. Fago said she thought it would help Mr. Trump’s chances of winning the election, according to two people familiar with the matter.

Richard G. Lubin, a lawyer for Ms. Fago, declined to comment.

On Sept. 3, Ms. Fago’s daughter alerted Project Veritas about the diary through its tip line.

Three days later, Ms. Harris and Mr. Kurlander — with the diary in hand — attended the fund-raiser attended by Donald Trump Jr. at Ms. Fago’s house in Jupiter, Fla., to see whether the president’s re-election campaign might be interested in it. While there, Mr. Kurlander showed others the diary. It is unclear who saw it.

After the criminal investigation into Project Veritas became public last fall, a prominent Republican lawyer who was lobbying on behalf of the organization and Mr. O’Keefe briefed a group of congressional Republicans on the case, to urge them to try to persuade the Justice Department to back off the investigation because the group did nothing wrong, according to a person briefed on the matter.

The lawyer, Mark Paoletta, said that upon learning about the diary at the fund-raiser, Donald Trump Jr. showed no interest in it and said that whoever was in possession of it should report it to the F.B.I. But shortly thereafter Mr. Paoletta, who had served as Vice President Mike Pence’s top lawyer in the White House, called back the congressional Republicans to say he was unsure whether the account about Donald Trump Jr.’s reaction was accurate.

Lobbying filings show that Mr. Paoletta was paid $50,000 during the last two months of last year to inform members of Congress about the F.B.I. raid on Mr. O’Keefe. Mr. Paoletta and a lawyer for Donald Trump Jr. did not respond to messages seeking comment.

Once Project Veritas learned about the diary in early September, the group sought to acquire it. About a week after the fund-raiser, Ms. Harris and Mr. Kurlander flew to New York with the diary. The pair met with several Project Veritas operatives at a hotel on Manhattan’s West Side.

The two sides began negotiating an agreement, but no final deal was struck at that stage and Ms. Harris and Mr. Kurlander returned to Florida. In response to questions about what Project Veritas may have asked him to do to help authenticate the diary, Mr. Kurlander, through his lawyer, Jonathan Kaplan, declined to comment.

But Project Veritas had to confront tricky questions: Was the diary really Ashley Biden’s, and not a fake or a setup? How could Project Veritas, best known for its undercover sting operations, be sure it was not a victim of its own deceptive tactics?

To authenticate the diary, one of Mr. O’Keefe’s top lieutenants, Spencer Meads, was dispatched to Florida to do more investigative work.

What happened next is a matter of dispute and one of the major issues in the investigation. Project Veritas has said in court filings that its operatives obtained additional items belonging to Ms. Biden that their “sources” had described as “abandoned,” suggesting that it had no knowledge of any theft and that it had gotten access to Ms. Biden’s belongings in the same way that journalists receive information.

“The sources arranged to meet the Project Veritas journalist in Florida soon thereafter to give the journalist additional abandoned items,” lawyers for the group wrote in a federal court filing.

Project Veritas’s lawyers had long instructed its operatives that encouraging or incentivizing sources to steal documents or items could ensnare the group in a crime. In a memo to Mr. O’Keefe in 2017, one of the group’s lawyers concluded: “Under controlling precedent, PV enjoys substantial legal protections to report and disclose material that may have been illegally obtained provided it played no part in obtaining it.”

But at least one of the “sources” told others that a Project Veritas operative had asked them whether they could retrieve more items from the home that could help show that the diary belonged to Ms. Biden, according to a person with knowledge of the exchange. Additional items were then taken out of the home and given to the operative, one of the sources has told others.

In response to assertions from Project Veritas that it had done nothing wrong and that its role in the case was protected by the First Amendment, prosecutors accused the group in court filings of making unsworn statements that are either “false or misleading and are directly contradicted by the evidence.” They also stated that even a legitimate news organization would have no First Amendment defense for acquiring material through theft or another crime.

“Put simply, even members of the news media ‘may not with impunity break and enter an office or dwelling to gather news,’” prosecutors said.

Without citing specific evidence, prosecutors directly challenged one argument from Project Veritas in particular: the group’s “repeated claim that they had ‘no involvement’ in how the victim’s property was ‘acquired.’”

The plan for Ms. Biden to have a friend retrieve the diary from the person who called her in early October fell through. And the accounts that Project Veritas has laid out in court papers and to the local police in Florida about how it obtained the diary and dealt with it in the final weeks leave open questions about how the events played out.

Project Veritas told a federal judge that on Oct. 12, Mr. O’Keefe sent an email telling his team that he had made the decision not to publish a story about the diary, adding, “We have no doubt the document is real” but that reactions to its publication would be “characterized as a cheap shot.” The date provided by Mr. O’Keefe for the email was shortly after the call to Ms. Biden.

But four days after Mr. O’Keefe told his staff that it would not publish the diary, a top lawyer for Project Veritas told Mr. Biden’s campaign that it had the diary and wanted to interview Mr. Biden on camera about it, The Times reported in December.

Less than a week after that, Project Veritas finalized a deal with Mr. Kurlander and Ms. Harris to buy the rights to publish the diary for $40,000, wired them the money and signaled that the group planned to soon publish it, according a person with knowledge of the case.

In the end, Project Veritas chose not to publish. Instead, an obscure right-wing website published the diary in late October, but it got little attention before the election. Mr. O’Keefe was furious, and some within Project Veritas thought that one of its own operatives, frustrated with the group’s unwillingness to publish the diary, had leaked it.

Project Veritas decided to have one of its operatives take the diary and Ms. Biden’s other belongings back to Florida.

According to a Delray Beach Police Department report, a lawyer showed up at the department and gave the items to an officer. The lawyer, according to police body camera footage, said the items were “possibly stolen.”

The police alerted the F.B.I., which had an agent retrieve Ms. Biden’s diary and other belongings. Almost a year later, the F.B.I. approached Ms. Harris and Mr. Kurlander.

About two weeks later, F.B.I. agents obtained search warrants to raid the homes of Mr. O’Keefe and two of his operatives: Mr. Meads and Eric Cochran, both of whom left the organization after the diary project. In the case of Mr. Meads, his lawyer said the F.B.I. broke down his apartment door. Court documents indicate that the F.B.I. seized 47 devices, including a dozen phones from Mr. Meads.

Kenneth P. Vogel and William K. Rashbaum contributed reporting. Matthew Cullen, Kitty Bennett and Kirsten Noyes contributed research.