You require approval from the BATF before moving a Title II device between states (temporarily to shoot it or to move.) I believe this is form [SIZE=-1]5320.20.[/SIZE]
You can take a can across state lines without having to file a Form 5320.20 like you would for a machine gun or SBR. Assuming, of course, that it is legal to possess said can in the state you're going to.
IIRC, suppressors do not need a transport form just to temporarily take it out of state. I think that's the only Title II firearm that's exempt from the Form. However, with any NFA device, if you are permanently changing your state of residence, you DO need to file with the BATFE.
Do you have a citation that you have to file for a permanent move? If the law doesn't require permission for interstate transport of suppressors or AOW's, you don't have have to get permission to move.