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according to the show, only the two of them know how to build the atomic bomb at this point
This is historical nonsense. Several physicists realised that an atomic bomb might be possible shortly after the discovery of nuclear fission, notably Leo Szilard, a Hungarian living in the USA. He enlisted Einstein to sign a letter in August 1939 to President Franklin D Roosevelt, warning that Nazi Germany might develop atomic bombs.
This letter was effective in starting the Manhattan Project, which developed the engineering and materials production technology needed to build the bomb. However, the scenario described is completely impossible for several reasons: