Authorities are trying to find out if fraud occurred when $600,000 raised at an amfAR auction went to the theater company that had produced Weinstein’s musical “Finding Neverland.” The musical is adapted from the 2004 whimsical film of the same name about a widow whose four young sons inspired playwright J.M. Barrie to write the children’s classic “Peter Pan.” The $20 million show failed to recoup.

Cole was a leader of amfAR, which stands for American Foundation for AIDS Research, at the time.

In a statement Thursday, the group didn’t mention the fraud allegation, saying only that Cole had served the group with “extraordinary dedication.”

“Under his leadership we have raised hundreds of millions of dollars for AIDS research, had a profound impact on millions of people’s lives and gotten closer to our ultimate goal of finding a cure for this insidious disease,” the statement read.

In his own statement, Cole said he had “proudly served” on the amfAR board and will serve as honorary chairman, helping elect the new chairman. He said he supported the board’s term limit reform.

Cole has had a long relationship with amfAR, joining its board in 1987. He was elected vice chairman in 2002 and chairman of the board three years later. He has also designed the group’s advertising, including the “We All Have AIDS” public service campaign in 2005.

Mr. Weinstein, who is a longtime supporter of the AIDS organization and was a chairman of the 2015 event, said that he had done nothing wrong and that everyone benefited from the arrangement, which raised $309,669 for amfAR. “I honestly thought we were doing something fantastic for both sides,” he said in an interview. “We get money, they get money, and it’s all our money.”

Gibson, Dunn & Cutcher, a law firm hired by the amfAR board, reviewed the $600,000 transaction and determined that it was legitimate and lawful.

But a lawyer who first investigated the way the arrangement was handled concluded that it put the charity’s financial integrity at risk, according to several people who reviewed his confidential report, which was commissioned by amfAR.

And in a June 2015 email to the charity’s chief financial officer, its chief executive, Kevin Frost, expressed concern: “Nothing about this deal feels right to me, and I believe we have not done due diligence to understand exactly what this money is being directed to or why amfAR is being used to facilitate these transfers.”

In April of this year, four members of the 19-person board complained to the attorney general’s office. They said that Kenneth Cole, the fashion designer and board chairman, had signed off on the $600,000 transfer “despite the clear objections of the executive management team,” said their spokesman, Steven Goldberg. They say board members were never informed that the auction proceeds would help cover the “Finding Neverland” investors’ costs.

Mr. Cole said that he welcomed an arrangement that would bring in money for the AIDS cause and that executive staff had signed off on it. He said that he did not recall Mr. Weinstein telling him it would serve a business deal with the American Repertory Theatre, but that he was satisfied knowing the $600,000 was going to a credible nonprofit.

“This wasn’t just a man on the street asking — it was someone who has raised a lot of money for us,” Mr. Cole said in an interview. “One tends to address requests based on whom they’re coming from.”

A staging of “Finding Neverland” that Mr. Weinstein produced at the American Repertory Theater in Cambridge, Mass. Credit Kayana Szymczak for The New York Times

It is not uncommon for commercial shows, before they hit Broadway, to go through an incubation period at a nonprofit theater, with infusions of financial support from investors. Under so-called enhancement agreements, the theaters are able to mount larger productions than their budgets normally allow, while producers and investors get feedback and a chance to polish their shows before going to New York.

What was unusual about the agreement that Mr. Weinstein’s theatrical production company, Weinstein Live Entertainment, struck in 2014 with the repertory theater — located in Cambridge, Mass., and affiliated with Harvard University — is that the show’s 24 investors would be reimbursed if they brought in third-party charitable contributions.

In the end, $1.95 million in contributions were made to the theater as “contemplated by the agreement,” according to a July 2015 email from a lawyer for the theater to Mr. Weinstein’s lawyer. In addition to the money that came from the amfAR auction, Mr. Weinstein helped arrange for a $200,000 donation from a family foundation that fights poverty in South Africa, a $600,000 donation from the Louis Vuitton fashion house and hundreds of thousands of dollars more from online charitable auctions.

Lloyd Mayer, a professor of nonprofit law at the University of Notre Dame, said the agreement appeared to allow charitable contributions to serve the private benefit of Mr. Weinstein and the other commercial investors.

Jason Lilien, Mr. Weinstein’s lawyer, said it did not matter if the other “Finding Neverland” investors “incidentally benefited” from the charitable contributions because the primary purpose was to put on a production for the public’s benefit. The theater declined to comment.

Mr. Lilien said Mr. Weinstein told Mr. Cole that the money raised through the auction would serve a “Finding Neverland” business agreement. Orin Snyder, a lawyer with Gibson, Dunn & Cutcher, said in a statement that “during our inquiry, Harvey Weinstein disclosed and we confirmed that the contribution was part of his company’s ‘Finding Neverland’ agreement with A.R.T.,” referring to the theater.

The auction catalog for the amfAR fund-raising gala disclosed that some of the money raised from the sitting with the fashion photographer would go to the theater, but did not note that for the Hollywood experience package arranged by Mr. Weinstein. Tom Ajamie, the first lawyer hired by the charity to review the $600,000 transaction, concluded that failure to disclose was “fraud on the bidders” by amfAR, according to people who reviewed the report. Mr. Weinstein’s attorneys said it was a clerical mistake by amfAR.

Mr. Weinstein said that when arranging the charitable contributions that flowed to the theater he told some donors that the funds were to support the “Finding Neverland” production. But, he said, it wasn’t his responsibility to further disclose that the money would be used to reimburse him and the other investors or otherwise cover their business obligations. If people wanted to learn more, he said, they could have done internet research.

“Today, if you want to know something, it’s easy,” he said. “Google ‘A.R.T.,’ whatever. You don’t want to make a donation to that, don’t. Whatever. These people aren’t forced to write a check to A.R.T. They can Google it, they can call it, they can speak to it, people will answer them.”

After Gibson, Dunn & Cutcher concluded its investigation, Mr. Weinstein asked amfAR board members and executive staff to sign pledges that there was no evidence of wrongdoing and that they would not probe further. In exchange, he said that he “will not at any time in the future engage in wrongful conduct involving amfAR.”

Explaining why he had sought the non-disclosures, Mr. Weinstein expressed annoyance, saying that he had been dragged into an internal power struggle on amfAR’s board. Four members — Vincent Roberti, Mervyn Silverman, Arlen Andelson and Jonathan Canno — refused to sign the document. The next month, they went to the attorney general. Since then, two other board members have resigned over the handling of the transaction, according to several people familiar with the resignations.

Mr. Weinstein has helped raise millions of dollars for amfAR over the years at its annual benefit at Cannes, which draws celebrities and is one of the most glamorous charitable events in the world. In 2016, he also helped arrange a fund-raiser for the organization in New York. This year, he pledged a $1 million in donations to the charity. Mr. Weinstein said he paid $600,000 of that commitment this year to try to smooth over the conflict.

“I went to them. I said, ‘I’m paying you $600,000 — shut up, you’re hurting the goddamn charity,’” he said.