Complex sentence: Following the Nazi invasion of Yugoslavia, from 1941 Radio Belgrade became "Soldatensender Belgrad" to entertain German armed forces; the song was played frequently and became popular throughout Europe and the Mediterranean among both Axis and Allied troops.
Split into simpler sentences: Following the Nazi invasion of Yugoslavia in 1941, Radio Belgrade became "Soldatensender Belgrad" and played the song frequently to entertain the German armed forces within its reach. It became popular throughout Europe and the Mediterranean among both Axis and Allied troops.