On top of the scope and also stamped onto the top of the Butts wrist by rights the rifles serial number will be on the section of wrist that fits into the butt socket but I suggest you leave it all alone and take it for granted like I have that the rifles serial number is there.
All the T's woods were marked so they stayed with the same rifle throughout the conversion process as if it was fitted with anothers woods chances of it passing the accuracy test may not happen.
Its a nice looking unit a range report is on the cards....