They may have one. If not, it may be possible to fit a modern Uberti repro stock to it. It may just better to buy a Henry buttplate and then have a smith fit it.
BTW, if you can trace the gun to a particular soldier, it may be worth a lot more. Try writing Winchester or some Winchester club and see if they've got serial #s to those Henrys. It is likely that yours was used during the American Civil War as Henrys were started up during the war and the majority were purchased privately by Union soldiers.
We've a local Henry that I traced to a soldier but he was a Lt. in the 2nd California so there's no great Civil War battle that it could have been involved in.
Congratulations on acquiring your "Damn Yankee rifle that you load on Sunday and shoot all week."