Very cool discovery. I’d say don’t restore it but stabilize it and display it in the visitor center.
My guess is, the rifle was abandoned by an old-timer who died somewhere nearby in the 1940s or 1950s at the latest, since those decades have suddenly gotten pretty far back in time. If the rifle had been propped against that tree for 130 years, I very much doubt it would be in this kind of shape, particularly the stock, which really doesn’t look too bad. Granted, we have much more rain around here, but being poor rural folk, we have a lot of experience with exposed 19th century wood. :’) Wow, that didn’t sound quite right.