Exhumis:  None of your pictures clearly show the Butt-plate area of your carbine stock.  The one picture that shows some of the Butt-plate looks like something might be altered.  The stylized "P" in a circle ("passed") stamp is common on Krag and Trap-door Springfield Stocks, behind the trigger guard.  The 1896 Carbine Stock is desireable to collectors doing restorations.  In the 1920s and 1930s loose carbine stocks were often put on shortened rifles to make sporters.  A real 1896 carbine will fall in specific serial # ranges, have a real Krag front-sight base, and be exactly 22 inches (measured from the muzzle to the closed bolt face.  The sling bar and ring were probably removed as being a nuisance to a hunter.  You inherited a nice family heirloom.  I'd keep and treasure it, as is.