I don't see why not.
It would depend on how handy your brother is and what his standards are as to how it looks when he's done..... the easiest would be to plan the length for a suitably sized slip on recoil pad and then fabricate a new backer where the stock gets cut so the slip on pad will have some support.
You might want to speak with Martin from Corwin Arms, he's pretty up to date on Turkish shotguns and might be able to point you towards a wood stock (easier to modify) or some other adjustable stock for Hatsan's.