As you have been informed the receiver markings and serial number range positively identifies your rifle as an A4. The barrel date is consistent with other A4's in that range so the so the barrel is most likely the original.

The AA mark is a depot rebuild mark which is quite common on A4's encountered today. Since the mark has been partially sanded out the stock may have been subsequently refinished.
If the rifle had come back in someones duffle bag the stock would have different markings, the bolt would be blued or black oxide and more than likely it would show some more signs of use.

Its a nice find and you should know that all A4's were marked "03-A3" the intention being that if they were not accurate enough for sniper duty standard iron sights could be installed and they would be issued as "03-A3" 's.

Regards,
Jim