Big hedge funds might have accepted the money even if they realized it belonged to Mr. Abramovich. At the time, the oligarch wasn’t under sanctions.

The manner in which one hedge fund received Mr. Abramovich’s money in the summer of 2012 shows the challenges facing U.S. and European authorities who hope to track down the assets of him and other oligarchs.

The manager of the fund, which oversaw billions of dollars but wasn’t a big name on Wall Street, provided a detailed accounting of his involvement on the condition that neither he nor his firm be named.

In 2012, a New York-based wealth manager at Credit Suisse, Gerald McGinley, contacted the fund manager on behalf of what he said was a wealthy family. Mr. McGinley said Concord was representing the family and was interested in investing tens of millions of dollars with the hedge fund.

The fund manager said Credit Suisse had told him that in order to receive the investment, he would have to set up a special financial vehicle in an offshore jurisdiction, so that the investment wouldn’t incur U.S. taxes. The hedge fund would receive a small percentage of the total investment as a fee, and Credit Suisse would get 20 percent of that fee.

Accompanied by one of Mr. McGinley’s colleagues at Credit Suisse, the fund manager traveled to Concord’s offices in a drab building in the New York City suburb of Tarrytown. Thick metal doors hid its offices from other occupants of the building. Inside, the walls were devoid of artwork or decorations.