Greetings and welcome to our little corner of the world!
Thank you for mentioning my earlier posts. Based on everything that I know, which is really pretty limited, you have it right. During this early period, LW usually stands for Landwehr, 2C would refer to the 2nd Company, and 564 would be the number of the weapon. With that information, a great deal of persistence and even more luck, you might be able to find some information about Landwehr Regiment 2. However.... you may not. You also might try looking for "Preußisches Infanterieregiment No. 2" or "Altpreußisches Infanterieregiment No. 2" because at the time this weapon would have been in the hands of a Landwehrmann, circa 1813-1860, each regiment usually, often, sometimes, maybe, had a Landwehr unit attached to it that was identified with the same number. Keep in mind that the designation of your weapon is to the same as K.und K. LW 2: that would be Austrian Landwehr Regiment Nr. 2. Yours is also not the same as LIR 2 which wasn't created until 1868. So, unless you're simply real curious, don't get trapped into following those leads during your search. The other marks on your weapon indicate that it was made at the Königliche Preußische Gewehrfabrique -- Suhl. You can find lots of interesting stuff about that too. You might want to start here:
https://de.wikipedia.org/wiki/Königliche_Preußische_Gewehrfabrique. Then you should also see:
https://de.wikipedia.org/wiki/Suhl (Suhl which is near Erfurt, is now so ashamed of its history that it declared itself officially a "city of peace) and finally and most importantly, see:
https://de.wikipedia.org/wiki/Infanteriegewehr_M/1809 This article will explain a little more about your weapon. If you find it by using a search engine (goo...) it will show an option for having it translated for you. But then.... the next question you might ask is .... how did it get here?
With a little more searching you'll find that after the outbreak of the Civil War in 1861, many of these obsolete weapons were sold to agents of both the north and the south. Most of them ended up going to the North and there are lots and lots of references to them in that connection. You might be lucky enough to find a state name stamped on the stock somewhere. For example, a lot of them went to Ohio and show a stamped "Ohio" somewhere on the stock. There are lots of other states that stamped theirs as well such as "Conn." and "Mass." If you look in federal records, there are lots of references to the purchase and distribution of them. Unfortunately, there isn't one source that collates them all. In general, most officers rejected them for use, so they were sent to the various states, each of which was clamoring for weapons to supply the regiments they were forming. If your example, has a state stamp, or you purchased yours in a state that received these weapons, you should be able to find accounts in your state's archives detailing the transfer to the state and then out to various units. They wont be so detailed to allow you to follow a given serial number, but you will be able to get an impression of the overall pattern within your state.
The next question you might consider, after all of that is "what do I do with it?" Well, the easiest thing would be to keep it like it is. It is a very nice example of military weapon. Its history and the changes it has endured reflect, in many ways, important events in history of the world. As it is, it can tell a very interesting story. Or, you could restore it. There is at least one source that used to make replacement stocks for Potsdam muskets. Your example was made in Suhl, but that is should not have any signficance when looking for a new stock. Howeve, the fact that yours had been cut down tells a story about firearms in the United States following the Civil War, when many military weapons were converted to civilian use and tastes. Restoring it could be an interesting and educational project. Or, you could have it done professionally. At the end of a professional restoration it would look like it was the day it was born. However, it would be very expensive and many people would argue that any "restoration" of an historic firearme destroys all value. Others point to the practice of restoring classic automobiles and explain that people have been restoring those for years. Whatever path you decide to follow, please let us know.
Finally, if you're very lucky and even more brave (some would use the word foolhardy or stupid), you might have one that is in good enough shape to
consider firing it! However, before you take that step, please do a couple of other things. First, make sure it is not loaded. I can't tell you how many times people are shocked to learn that an old muzzleloader they've had around for years is still loaded. Put a rod or measuring tape down the inside of the barrel and see how far you get. You should be able to tell from this if it is loaded or otherwise obstructed. Second, take it to someone who is extremely knowledgable concerning muzzleloaders and ask for an opinion. Ask them if it would be safe to fire. Third, if the "expert" indicates it would be safe, put together some sort of clamping system, often an old tire on a table will work, that will allow you tie it or clamp it down securely so that you can
stand a safe distance away and fire it without holding it! If you get that far, please remember a camera: we would like to see the pictures. Until then, thank you again for your question and keep us posted as to what you discover.