no C stocks were ever used on 1903A3,s the only rifle that ever was issued with a C stock would be an 1903A4..
that being said, have no idea what a type 13 stock is, maybe some secret code that Joe Poyer uses..
id be leary of anyone offering original C stocks...SC used a standard S stock as well, made by many subcontractors, American Billiard was one of those makers, as was Keystone.
Remington supplied stocks for a small run of SC A3,s i have seen original rifles marked correctly with Remington made stocks. with SC markings.