Hi MJ,
Welcome to ALR. McLemore barrels are highly regarded. Mr. McLemore is/was known for making "gain" twist rifled barrels. Initially, and this is a wild guess, I thought maybe the "419 .31" markings could have something to do with gain twist. But apparently Mr. McLemore was somewhat secretive about the amount of gain in his barrels, so I don't know if he would stamp it on the barrel. The barrel is also marked ".50 C" which probably indicates .50 caliber. If you could measure the outside diameter of the barrel, flat to flat, that will help indicate it's intended purpose.
As for the stock, it looks like a Lancaster or York, PA pattern to me. You could compare it to the many stock patterns offered at
http://knobmountainmuzzleloading.com/stocks.htmlDid your Dad build guns? You might look around some more for a cigar box or shoe box of parts. You my find the smaller parts (lock, trigger, trigger guard, butt plate, etc.) for a complete rifle!
Good luck,
Ron