smd189, below is a clip from a message I recently sent to a fellow M-1865 owner. I hope it will be helpful.
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Surprisingly enough, most of the late delivery arms sat in storage until they were sold off as surplus. Spencers tended to get issued more than most, but even they were available in numbers way beyond the requirements of the Army. The army went from over 1 million in 1865 (plus almost a million Confederates) down to 25 thousand by 1875. There were enough Burnside made Spencer M-1865s to give one to every member of the post war army, even the cooks, clerks and generals. Plus there were enough Spencer made M-1865s, plus 60,000 or so M-1860 Spencers, plus equal numbers of about 15 other carbine types, plus 400,000 Enfield P-53 muskets, and 700,000 Springfield M-1861/'63/'64 muskets. The numbers are staggering!
When the Franco-Prussian war broke out in 1870, the US remained officially neutral, but the Ordnance Department took advantage of the situation to unload tens of thousands of brand new, surplus Civil War arms into Europe. This was done by holding large surplus sales and looking the other way while the buyers (principally Remington, Bannerman and Hartley & Graham) shipped their purchases off to France. Spencers were especially popular with French agents.
Frances' early defeat meant that most of the imported US arms were never issued there. Germany sold a lot of the US guns back to the same people that France bought them from a year earlier. Still, as late as the 1980s, Val Forgett (of Navy Arms) was discovering unopened cases of US Civil War carbines in the armories of France. Large numbers of M-1866 Springfields, Spencer carbines and all of the Burnside/Spencer/Springfield 2 band rifles went to Europe and came back to the US in the 1870s.
That's not a lot to go on, but I hope it helps. If you'd like to dig deeper into the subject, I'd recommend "Civil War Guns" by Edwards. It originally came out in the 1960s for the centennial and is rather dated today, but it's a classic, with lots of information on how the guns got made, and what happened to them after the war.
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Check the barrel length of your carbine. An M-1860 should be 22" when measured inside the bore. A post war model will be 20". Also, post war models were marked on top of the barrel between the rear sight and the frame; M-1865, M-1867 or N.M. A few were not narked, but that is quite unusual.
A lot of carbines were issued experimentally after the war, so the Spencers tended to be shipped out and then called back as companies tried 50-70 Sharps, Peabodys, M-1870 Trapdoors, Rolling Blocks, Ward-Burtons etc. etc. Herbert is right about teamsters, scouts and settlers getting Spencers when the natives were restless. Even Indian scouts and police got them from time to time.