A very nice Victorian English made shotgun. One of a pair, there should be another to match it. If the case will not take two guns then it is almost certainly a replacement. possibly doctored up with an original label. As you say the case has been relined and probably quite recently.
Have a knowledgeable gunsmith sheck out the barrels and anything else that may worry you. It should be fit to shoot if you stick to Black Powder Loads only. That will almost certainly mean handloading, but if I owned it, I wouldn't mind that chore. Any range you go to in the USA you will very likely be the only person present with an Alexander Henry shotgun.
Harry
