All of the clubs that I have played in state that you cannot move a newly captured aa gun during noncombat. One example is here, at the AAMC site (geesh, I didn’t even know this still existed lol).
http://www.aamc.net/bunker/aaruleclrfd.htm
If you scroll down to the section labeled “Antiaircaft Guns”, you will see “Six important gun facts are: 1. If you capture an enemy AA gun during your combat movement, you cannot move that AA gun during the non-combat phase of the same turn.”
This was the case in all PBEM clubs (play by e-mail) as well as the CD clubs. I think there was an official clarification by Larry Harris somewhere, but perhaps Krieghund could confirm that for me.
So, I would say that the move is illegal.