The Army List has your father listed as a W.S./Capt. on 25.07.1945 and as a T/Maj. on 25.07.1946. That would explain his epaulettes. The 2 photo's you posted of your father show him wearing the 3 pips of a Captain. Your father was commissioned into the A.A.C. Suggesting he was selected from the ranks of The Parachute Regiment for having demonstrated both bravery and leadership ability of a high level. As a newly commissioned officer, he didn't necessarily, probably didn't, return to his former battalion. He may have served with two Parachute battalions.