Complex sentence: When Miller broke up his band and entered the armed forces in 1942, recruiting music personnel for the Army Air Forces, he was able to secure Alpert, after his enlistment, by swapping ten musicians from Miller's own platoon.
Split into simpler sentences: When Miller broke up his band and entered the armed forces in 1942, he was recruiting music personnel for the Army Air Forces. Miller was able to secure Alpert after his enlistment by swapping ten musicians from Miller's own platoon.