Factory half mags or 2/3 mags had a domed "button" end, from the pics yours looks like a flat end. So either a full length magazine tube or the right magazine cap would be better. But the issue of the mismatched parts will count against that gun either way. From the looks of the front sight base, it has a post-war (produced after WW2) carbine barrel on it the original barrel for an 1898 rifle would have been different. If so, look at the underside of the barrel about 2"-3" from the muzzle it may have a small notch where the other barrel band would have been. It has a carbine forearm and a rifle buttstock (I would guess this repair was done by someone who could not cut the notch for a barrel tenon used to hold the rifle forend on or who had a carbine barrel and forearm sitting close at hand). Remember, many old Winchesters were working guns, not collector items until recently.
Without the letter frorm the Buffalo Bill museum, you would not know which it was, so you would not know which way to repair it (whether to repair it to look like a carbine or a rifle).