Still, the tax deduction is always greater if the donation goes to a public charity, like a university, hospital or, yes, a donor-advised fund, Ms. Snow said.

In the case of the Fairbairns, the $100 million donation included shares of Energous, which makes wireless charging technology. The shares had appreciated substantially on the regulatory approval of the company’s transmitter.

By using a donor-advised fund, the Fairbairns would not have to pay taxes on the capital gains in those shares. They would also receive a higher tax deduction for both the stock and cash portion, and ultimately be able to give more to charities as the stock price rose.

Or that was the plan.

The Fairbairns’ complaint alleges that Justin Kunz, a relationship manager in Fidelity’s family office group, which serves its wealthiest clients, made certain promises over how the donation would be handled. One of those promises, the suit says, was to sell the stock over time and not let any sale exceed 10 percent of the daily trading volume. A quick sale would decrease the value of the shares and whittle down the $100 million.

Vincent Loporchio, a spokesman for Fidelity Charitable, declined to make Mr. Kunz or anyone from Fidelity Charitable available for an interview. But in emails, he disputed the Fairbairns’ claims. He said that it was Fidelity Charitable’s policy to sell any securities as soon as they were received and that the Fairbairns had known this.

“Their claim that they were told something different is entirely false, and not supported by any evidence,” Mr. Loporchio said in an email.

The Fairbairns’ lawyers would not comment on the case, but they contested Fidelity’s response in their legal filings. They argued that Mr. Kunz and another executive at Fidelity Charitable who handled complex assets had told the Fairbairns that the stock would be sold gradually to maintain the price.