A Wave, a WAC and a Marine (movie, 1944)

Henny Brown, talent scout for the Margaret Ames Film Agency in Hollywood, mistakes Broadway show understudies Judy and Marian, for stars Betty and Eileen, and signs them up for movies. Margaret, furious with Henny for the blunder, fires him---but only temporarily. Another agent, Marty Allen, once married to and still in love with Margaret, signs Betty and Eileen. Henny arrives with Judy and Marian, and the nightclub manager asks Henny to emcee the show. Though he is not sure himself what they can do, Henny introduces the girls and they make a hit in a dramatic sketch. Big-time movie producer R. J. signs them to a film contract. Judy joins the WAVES, Marian the WACS and Marty the Marines and all have two weeks before induction, and that is more than long enough to shoot a Monogram musical-within-a-Monogram musical and have a few days to spare.