Not long before FTX collapsed in November, its founder, Sam Bankman-Fried, sent $400 million to an obscure cryptocurrency trading firm called Modulo Capital.

The fledgling firm, which was founded in March and operated out of the same Bahamian compound where Mr. Bankman-Fried lived, had no track record or public profile. One of the founders, Duncan Rheingans-Yoo, was only two years out of college. His business partner, Xiaoyun Zhang, known as Lily, was a former Wall Street trader who had previously been romantically involved with Mr. Bankman-Fried, according to four people with knowledge of their relationship.

Now, Modulo is emerging as a crucial part of the investigation by federal prosecutors into Mr. Bankman-Fried and his once giant cryptocurrency exchange. They’re examining whether he used FTX’s customer funds to invest in the little-known firm when his existing hedge fund, Alameda Research, was struggling amid a wider crypto industry downturn. The $400 million outlay was one of Mr. Bankman-Fried’s single largest investments.

At the same time, lawyers for FTX’s new leadership are eyeing Modulo’s assets as they scramble to recover the billions of dollars that customers, lenders and investors lost when the exchange imploded.

It’s unclear how much of FTX’s $400 million investment remains or where it is. But the authorities have been aware of the trading firm for months; the day after Mr. Bankman-Fried was arrested in the Bahamas in mid-December, he was denied bail at a court hearing where a local prosecutor argued that he was a flight risk and suggested he might be able to tap the funds sitting with Modulo.

Before starting Modulo, Ms. Zhang and Mr. Rheingans-Yoo worked at Jane Street, the Wall Street firm where Mr. Bankman-Fried, 30, began his career and met many of the people, in their 20s and 30s, who would later help him build his crypto empire.

It’s unclear how much money Modulo had other than Mr. Bankman-Fried’s investment. But it began trading crypto before FTX failed, and it has now largely shut down, according to a person familiar with its operations.

Mr. Bankman-Fried’s decision to provide so much funding to a start-up trading firm at the same time that Alameda was losing money raised suspicions for investigators.

At the bail hearing in Nassau, the local prosecutor cited an affidavit compiled by another Bahamian law enforcement official that has been under seal in court in the Bahamas. Federal prosecutors in Manhattan investigating Mr. Bankman-Fried believe the Modulo investment was made using criminal proceeds — misappropriated money that FTX customers had deposited with the exchange, said a person briefed on the investigation.

Neither of Modulo’s two founders has been accused of wrongdoing, but they recently hired Aitan Goelman, a criminal defense lawyer who is a former director of enforcement for the Commodity Futures Trading Commission. Mr. Goelman said he had no comment.

Representatives for FTX, Mr. Bankman-Fried and the U.S. attorney for the Southern District of New York in Manhattan all declined to comment.

The flow of money to Modulo has also caught the attention of the lawyers representing FTX in the company’s bankruptcy proceeding in Delaware. In a slide presentation to the exchange’s creditors that was filed in court last Tuesday, FTX’s lawyers flagged the transaction with Modulo as one of its prime targets for reclaiming money.

The presentation said Modulo received funds in installments in the third and fourth quarters of last year. Around $300 million of that total was transferred shortly before FTX’s implosion, according to the Bahamian prosecutor.

The payments occurred during a period when transfers of money can be challenged and potentially clawed back in the bankruptcy process. Clawback lawsuits are a powerful tool in bankruptcies to recover assets, and they played a crucial role in helping the victims of Bernard Madoff’s Ponzi scheme recoup much of the $19 billion that was invested in that decades-long fraud.

“Focusing on large, questionable transactions to a fund, company or a person with close connections to the debtor before the bankruptcy filing is basically the low-hanging fruit in a bankruptcy case,” said Lindsey Simon, a corporate law and bankruptcy professor at the University of Georgia School of Law.

Last week, FTX’s lawyers said they had found $5.5 billion in cash, securities and digital assets held in customer accounts or tucked away in other parts of the company. But the actual value of many of the cryptocurrencies owned by FTX is hard to determine, and the lawyers said the company still had a major shortfall in assets.

On Friday, federal prosecutors disclosed that they had seized more than $600 million in assets belonging to Mr. Bankman-Fried, including a mix of cash and stocks kept in bank and brokerage accounts.

Any legal action to reclaim the Modulo funds could provide a template for broader efforts to recover money that Mr. Bankman-Fried invested in smaller companies. At the height of his wealth and power, he funneled an estimated $4.6 billion into more than 300 companies, including an artificial intelligence start-up called Anthropic and the crypto company Yuga Labs.

Even amid that spending spree, the Modulo deal stands out because of the amount of money involved and Mr. Bankman-Fried’s close ties to the firm’s founders. Ms. Zhang and Mr. Rheingans-Yoo were also Modulo’s only directors, according to incorporation papers filed in the Bahamas.

Both left Jane Street last January, according to brokerage industry records, about three months before Modulo was incorporated. (Modulo has no connection with a similarly named investment firm in Brazil.)

A 2012 graduate of Amherst College, Ms. Zhang worked at Jane Street for a decade, overlapping with Mr. Bankman-Fried, who spent about three years there after graduating from the Massachusetts Institute of Technology in 2014. Mr. Rheingans-Yoo was a trader at Jane Street from 2020 to 2022, joining shortly after he graduated from Harvard, where he was captain of the fencing team. The crypto publication CoinDesk previously reported that Modulo’s founders had worked at Jane Street but did not identify them.

Before Modulo received the $400 million, the investment was the subject of debate within Mr. Bankman-Fried’s tight circle of top advisers, according to two people familiar with the discussions.

Ultimately, Mr. Bankman-Fried moved forward despite reservations voiced by Caroline Ellison, the 28-year-old chief executive of Alameda, other people familiar with the matter said. Ms. Ellison has since pleaded guilty to fraud charges for her role in FTX’s collapse and is cooperating with prosecutors in the criminal case against Mr. Bankman-Fried.

Further complicating the Modulo investment were the romantic ties among the executives involved in the deal. Ms. Ellison and Mr. Bankman-Fried had dated in the past, and they lived together with eight other roommates in a luxury penthouse at Albany, an oceanside resort on the Bahamian island of New Providence.

Mr. Bankman-Fried had also had a brief romantic relationship with Ms. Zhang when they worked together at Jane Street, one of the people with knowledge of the relationship said. By the time of the investment in Modulo, Mr. Bankman-Fried was not dating either woman, this person said.

Last spring, Modulo set up an office in the same Albany resort where Mr. Bankman-Fried and Ms. Ellison lived. Ms. Zhang and Mr. Bankman-Fried were still friends, and they would sometimes travel together on charter flights to New York from the Bahamas, according to two people familiar with the arrangements.

Mr. Bankman-Fried began to pour money into Modulo at a time when Alameda was struggling. After the crypto market crashed in May, a number of crypto lenders recalled their loans to Alameda, prompting the trading firm to pull money from FTX customer accounts to make up for the shortfall, according to federal prosecutors, regulators and former Alameda employees.

Sometime around September, Mr. Bankman-Fried was seriously considering shutting down Alameda, according to public charging documents, as well as private government records obtained by The New York Times. At the time, Alameda had lost $5 billion, which Mr. Bankman-Fried acknowledged to colleagues was more than the company had ever made or was likely to make in the future, the government records said. But he also expressed concerns about how FTX would function without Alameda trading on it.

The connections between FTX and the Modulo founders went beyond Mr. Bankman-Fried’s relationship with Ms. Zhang. Last year, FTX also hired Mr. Rheingans-Yoo’s older brother, Ross Rheingans-Yoo, from Jane Street to take a top job at the FTX Foundation, a charitable group funded by Mr. Bankman-Fried.

Ross Rheingans-Yoo, who graduated from Harvard in 2016, worked on the foundation’s pandemic preparedness efforts, according to a page on his personal website that is no longer active. There is no indication that he had anything to do with Modulo, and he did not respond to a request for comment.

But his charitable work aligned closely with the priorities of Mr. Bankman-Fried’s younger brother, Gabe Bankman-Fried, who ran Guarding Against Pandemics, an advocacy group that FTX helped bankroll. Both Rheingans-Yoo brothers, according to archived versions of their personal biography pages, were supporters of the principles of effective altruism, a philanthropic movement that urges adherents to donate the bulk of their income to charity and use data-driven analysis to maximize the impact of the contributions.

Mr. Bankman-Fried had also aligned himself with the movement. For years, he invoked his commitment to effective altruism as he cultivated a global brand, claiming that he got into crypto trading to make billions of dollars for worthy causes.

Kitty Bennett and Alain Delaquérière contributed research.