It is the brass buttplate from a Henry .44 Repeating Rifle, model-1860. The key ID clues are the circular flip-up cover in the BRASS butt's center, and the square-bodied tang. Approximately 14,000 Henry repeating rifles were manufactured between 1860 and 1866, and were used by both sides in the civil war. The serial number 13,795 on your Henry buttplate is near the very end of the 14,000 made, so yours is probably from 1866.
The Henry Rifle continued to be used by some US cavalrymen (and believe it or not, some Indians) into the 1870s. A number of Henry cartridge-casings were recovered by US National Park Service archeologists at the Custer's Little Bighorn battlefield (1876). Henry .44 ammunition was still being manufactured in the 1890s.
I'm just going to ad that the covered hole in the butt plate is not a loading port like a Spencer. It's for the cleaning rod. Black powder is foul burning and keeping
the gun clean was very important. For best accuracy some folks wipe the bore between every shot.