Complex sentence: After the World War II ended she was promoted to the rank of Captain and became the first women to be assigned to the U.S. Army Caribbean at Quarry Heights in the Panama Canal Zone, becoming the first woman to serve in this theater.
Split into simpler sentences: After the World War II ended, she was promoted to the rank of Captain. She was assigned to the U.S. Army Caribbean at Quarry Heights in the Panama Canal Zone, becoming the first woman to serve in this theater.