Think of it this way:
Once you are retreating units out of combat, they may not perform any more action(s) that turn. Their only action is to move 1 step to an adjacent space (planes excepted).
I in invade Western Europe with England and bring an AA-gun. Next turn Germany retakes Western Europe. What about the aa-gun. Is he allowed to move the aa-gun back to Germany og southern Europe in the same turn he invaded Western Europe?
You cannot move an AA gun you captured on the same turn.
The logic being:
The AA Gun was technically involved in a Combat (even if it did not fire at planes during the combat), so it cannot make a Non-combat move. The only pieces that defy this general rule are planes (explicitly excepted in the rulebook) and Panzerblitzing German tanks (German National Advantage - also explicitly excepted.)
This might also be explained as a common behaviour of the grey pieces - AA Guns and Complexes - in that if they are captured or liberated, the new owner doesn’t assume functional control of them until the end of the turn during which their capture or liberation occurred. I actually like this justification better than the one above.
The above posters are correct, the AA cannot be moved in the same turn it is captured.
Another “rule rationalization” reason for it:
No land units are permitted to retreat from a combat zone after the battle is over.