Soooo...on doing a bit more research for ya...it looks like there's some conflicting evidence. Looks like the division stationed at Fort Yellowstone was Troop M/1st Cavalry whereas Troop H/1st Cavalry was stationed at Fort Assiniboine, MT (late 1800s period). The website link reference could be wrong then. Token shown is obviously yours, but from what location exactly may require a bit more digging. I'm leaning toward the Fort Assiniboine location. I leave the rest up to you! Hope that helps you out.
John