Complex sentence: He then moved to Hollywood writing for stage musicals and films throughout the 1940s and early 1950s, winning an Academy Award for Best Original Song for "Swinging on a Star" (1944).
Split into simpler sentences: He then moved to Hollywood to write for films throughout the 1940s and early 1950s. He won an Academy Award for Best Original Song for "Swinging on a Star" (1944).