Updated July 14, 2015 12:54 p.m. ET

by RACHEL LOUISE ENSIGN

When lawyers with the district attorney’s office in Queens, N.Y., need to get documents to court, they sometimes load up carts and push them across the six bustling lanes of Queens Boulevard.

But the agency may soon be able to send the carts to the scrapyard: The Queens prosecutor’s office is set to collect $116 million as its share of HSBC Holdings PLC’s landmark $1.9 billion 2012 settlement related to allegations Latin American drug cartels laundered money through the bank. The agency, which hopes to use the money for new office space, was quietly awarded the funds because one of its investigators—a former beat cop called Frankie D. by his friends—first noticed the suspicious money flows in the bank’s accounts.

The Queens House of Detention in New York City. The local district attorney wants to use the property to expand his offices.

The payment, which hasn’t been previously reported, is one of the more unlikely windfalls to trickle down to the local level out of the tens of billions of dollars in penalties global banks have paid in recent years tied to charges of misbehavior.

The Treasury Department also awarded money to 20 other agencies involved in the HSBC probe, including $1.9 million to the Fort Lee, N.J., police department and $13.1 million for the Port Authority of New York and New Jersey, according to documents obtained through a public-records request. Some of the agencies say they are still figuring out how to spend the funds.

The Queens award, more than twice the office’s annual budget, was by far the largest to a local agency. The office hopes to spend the money in part on converting into an office the 467-bed Queens House of Detention, which sits next to the borough’s criminal courthouse. The jail is now largely empty and is often used as a set for movies and television shows, including “Orange Is the New Black.”

District Attorney Richard Brown has long dreamed of pursuing the project. “Every night when I go home from this office, pass by the Queens House and see seven or eight floors totally dark, I just say to myself, ‘What a perfect spot this is for our needs,’ ” he said.

The prosecutor’s office has outgrown its original quarters in the criminal courthouse, adding two satellite offices. Officials say all three spaces are now extremely overcrowded and in need of new equipment.

There is a potential snag: New York City, which would need to approve the renovation plan, isn’t backing the project. The mayor’s Office of Criminal Justice Director Elizabeth Glazer in May told Mr. Brown that the city is still using the property for jail operations and wants to find the district attorney other space, according to an email Ms. Glazer sent to the district attorney that was reviewed by The Wall Street Journal. Mr. Brown said his office doesn’t consider that “a definitive answer.”

As part of its pact with a handful of U.S. authorities, HSBC admitted that it failed to catch at least $881 million in drug-trafficking proceeds laundered through its U.S. bank and that its staff stripped data from transactions with Iran, Libya and Sudan to evade U.S. sanctions. It also agreed to enter into a five-year deferred-prosecution agreement.

The money-laundering probe likely would have never have gotten off the ground if not for investigator Frank DiGregorio, according to people involved in the case.

Queens District Attorney Richard Brown’s office helped investigate money laundering by bank HSBC Holdings, earning the New York City agency a sizable chunk of the related settlement.

Mr. DiGregorio, a gregarious New Yorker who sports a deep tan from days spent fishing for sharks, is a former beat cop in Brooklyn and Queens who in the 1980s probed organized-crime involvement in the city’s garbage industry. He says money launderers once put out a contract on his life.

Since 2005, the 61-year-old has led a team on the El Dorado Task Force that tracks money laundering in the drug trade. The financial-crimes task force is staffed by employees from more than 50 New York-area agencies and is run by the investigative arm of the Department of Homeland Security.

After the 2001 Patriot Act required U.S. banks to tighten money-laundering controls, Mr. DiGregorio and his team noticed a big uptick in flows of dollars to and from Mexico. They discovered, on digging further, that drug money was increasingly being laundered using large cash deposits in Mexican banks, including HSBC’s Mexican subsidiary, according to Mr. DiGregorio and court records. That money often ran through HSBC’s U.S. affiliate, court documents show.

“There had been a lot of bank cases but nowhere near what this one was like,” Mr. DiGregorio said, adding it was “very satisfying” to see the bank pay a big penalty. “For me, I don’t get 50 cents out of that money, but I think it had an echo effect throughout the major banks. They all now stop to say, ‘What are we doing wrong?’ ”

Queens was eligible for its payment because state and local law-enforcement agencies can get a cut of money or property forfeited to the federal government if they played a role in the case. The office won its huge award because its staffers, including Mr. DiGregorio, spent more than 5,000 hours on the case, according to Treasury Department documents.

The Treasury’s program applied to part of HSBC’s forfeiture of $1.26 billion as part of the settlement. The other $665 million was a civil penalty that went into the Treasury’s general fund.

The Queens prosecutor’s office has to submit detailed plans to the Treasury to receive most of the money. The office has already gotten about $49 million, which will be spent on a cybercrime lab, new telephone system and other upgrades. For now, the district attorney continues to hold news conferences and meetings in a conference room that shares a wall with the empty jail.

“The folklore has it that, at one time, some of the inmates tried to break out of the Queens House by breaking through the wall that’s right in front of you over there,” Mr. Brown said, pointing at the common wall. “It just seems to me very obvious that space is just going to total waste.”

Write to Rachel Louise Ensign at rachel.ensign@wsj.com