Final answer:
The Soviet Union moved troops to assist the Allies in invading Japan's largest islands while the atomic bombs were dropped. President Roosevelt approved the funding for the Manhattan Project after receiving a letter from Albert Einstein and Leo Szilard.
Step-by-step explanation:
The country that was moving troops over to assist the other Allies in an invasion of Japan's largest islands when the atomic bombs were dropped was the Soviet Union. They declared war on Japan on August 8, 1945 and began their invasion of Manchuria in order to push back Japanese forces.
President Roosevelt approved the funding for the Manhattan Project after receiving a letter from Albert Einstein and physicist Leo Szilard. In this letter, they warned him about the possibility of Germany building an atomic bomb and emphasized the importance of American research and development in this field.
Learn more about Invasion of Japan's largest islands and the Manhattan Project