The Buffalo Bill Cody Museum in WY would be the place you would need to contact to fine that they have all that information now. That is in Cody WY sorry I don't have the address or a phone number. But I am sure they charge a fee for doing the research as I wanted them to look up the history on a Marlin 1893 rifle I have. I chose not to do it and I don't remember how much the fee was.
Good evening. My name is ***** ***** I am one of the firearms experts here. While the Cody Museum does have some firearms records, they do not have records of the Springfield Armory Model 1873 Trapdoor rifle. Unfortunately, any records of who the gun was issued to are probably lost to time. You may be able to file a FOIA request with the United States Army to see of they have any records, but I doubt seriously that you would get far. I can give you the values of your rifle if you are interested.....just let me know.