Complex sentence: Bauman went on to serve in the Soviet-controlled Polish First Army, working as a political education instructor and taking part in the battles of Kolberg (now Kołobrzeg) and Berlin.
Split into simpler sentences: Bauman went on to serve in the Soviet-controlled Polish First Army, working as a political education instructor. He took part in the battles of Kolberg (now Kołobrzeg) and Berlin.