I think the box must have been custom built for that revolver some time after the gun was acquired. I have never seen one like that which could be established as original. If it is custom built, the earlier it was built the likelier it is the revolver was purchased without the detachable stock; the later the box's construction, the likelier the separate stock was lost or damaged before the owner decided to take care of what was left.
Could I ask you to confirm that the barrel is 16 inches long from breech end to muzzle and omitting the cylinder? I tried to allow for perspective distortion in the image, but it looks more like 14 inches to me. If so, that may mean the gun was special ordered with a short barrel and no buttstock or that the barrel was shortened later for some reason. I have a cut down RR that now has no stock and an eight-inch barrel -- basically just a crudely fashioned target revolver that was cut out of something larger and better. The rib was milled off the barrel and the frame was contoured so that a forearm piece can no longer be attached. It's an ugly and tragic mess, but my gun and others that I have heard about are evidence that people modified these interesting firearms in unanticipated ways.
I am not sure what value to put on what I see in the picture. A complete and unmodified rifle in its original case that I know about sold for $7000 two or three years ago, but it has little of its original finish left, needs some light smithing, and the plywood and fabric case is kind of ratty after 130 years. I picked up the butchered RR I mentioned for a little under two grand. Your gun appears nice but is incomplete, so I'm guessing the package I see should be valued somewhere between $5000-9000. I can't tell if it has been refinished -- many were -- but if so that would hold collector value down. If the letter reveals interesting details -- special order configuration, sold to an interesting person, that kind of thing -- the value could go higher. It's good that you have the ammunition. That stuff is not commonly seen. If you can get value estimates from others, average what you hear from everyone and you will probably be close to reasonable valuation.
Congratulations on owning that one. The 320 RRs were a long way from being S&W's most successful model, but are certainly one of the most interesting ones.