In August 1941, German-born Klaus Fuchs (a passionate dedicated Communist) was recruited in Britain by the GRU (Red Army Intelligence), and Fuchs became a key source for Moscow Centre ("Spy Central"). Soon after Pearl Harbor, Moscow learned from Fuchs (and other sources) that the British had abandoned their atomic research, leaving the U.S. and the Manhattan Project as the only show in town. J. Robert Oppenheimer (the scientific head of the Manhattan Project) unwittingly gave some crucial hints to a Soviet spy while at a social occasion attended by left-wingers; among the tidbits from Oppenheimer were Einstein's letter to FDR in 1939. The NKVD (the precursor to the KGB) gave Oppenheimer the codename "Star", knowing that some of Oppenheimer's closest friends and many acquaintances were left-wingers, and many of them were Soviet spies/informants.
General Leslie Groves. Afterwards, the "approaches" to Oppenheimer were drastically reduced, but not entirely eliminated. In his memoirs, one Soviet spy asserted that Leo Szilard, Enrico Fermi, and Oppenheimer knowingly assisted the NKVD in placing moles in various laboratories associated with the Manhattan Project. The same spy claimed that Oppenheimer requested the services of Fuchs knowing he was a Soviet spy. Both those assertions are most likely incredibly impossible, but since Oppenheimer in 1954 lied about his past associations with Communists, many were (and are) ready to believe the worst about him.
If nothing else, Oppenheimer (like Harry Hopkins, one of FDR's most trusted aids) was guilty of some moronic indiscretions which served, in effect, to be the base equivalent of actually being a Soviet informant. By 1942, Moscow was alarmed that the U.S. had committed so much money and resources to the Manhattan Project. Stalin, far more than Winston Churchill or FDR, grasped the strategic significance of the atomic bomb after World War II, and he was hellbent on finding out as much as possible about what was going on with America's atomic research.
By 1943 Moscow was still learning more about the Manhattan Project from British informants compared to American informants. Among those informants in Britain were Klaus Fuchs, but he wasn't the only source of information in Great Britain for Moscow. In early 1944, Moscow gave their intelligence operation the codename "Enormoz".
During the Winter of 1943, Fuchs was posted in the U.S., and for a while the USSR had a steady stream of information. By 1944, the USSR was conducting technical espionage on an industrial scale; Moscow wasn't just getting information on atomic bomb research, but also on radar, wireless technology, jet propulsion, and synthetic rubber. After a surprise junket to Britain, Fuchs returned to the U.S. in November 1944 . . . and Fuchs was working in New Mexico. Fuchs kept providing information and all he wanted in return was to have the files the Gestapo had on him destroyed when the Red Army reached Berlin.
By the Spring of 1945, Moscow was receiving a steady stream of intelligence from both British and American spies/informants, but by then U.S. security measures were improving, making it more difficult for NKVD handlers to meet with their sources (among the second-tier sources for Moscow was Julius Rosenberg). Twelve days before the bomb that was used for the Trinity Test was assembled, the USSR had secured descriptions of the atomic bomb from their New York City (Fuchs) and Washington, D.C. stations, and in just four years, the USSR would successfully test their first atomic bomb, ending the four year U.S. nuclear monopoly.