Complex sentence: The group was moved to the Eastern front at the start of the Invasion of Poland, moving back to the Western Front later as III Gruppe of Jagdgeschwader 51 (III./JG 51).
Split into simpler sentences: The group was moved to Eastern front at the start of Invasion of Poland. Later it was moved back to Western Front as group III of Jagdgeschwader 51 (III./JG 51).