I find myself in a peculiar position. I have studied several original Jacob Kuntz rifles and pistols in hand, and many more from publications. This is what turned me on to build one. The best I can do regarding this subject is to offer my impressions, based on a couple of not particularly good photos.
I agree that at least the lid and head of the patch box, and the cheek piece inlay, are by Jacob Kuntz. He used bone, horn, and other materials for inlays and embellishments on many of his rifles, so the side plates of the box may also be by his hand.
The stock's architecture is a departure from his flint era longrifles, and being walnut also is different. There are two details about the carving that are giving me a red flag. the first and more important one is the carving behind the cheek piece. It does not have the artistic merit I've come to love about his work. The elements of the carving are rough and don't have the flow I'd expect to see by Jacob Kuntz. I don't think he carved it. Secondly, the lock molding is thick and abrupt, and again, does not look like his work. The comb from the butt plate's heel to the wrist is not up to Kuntz standard either.
More pictures, or the side plate side of the lock area, the toe plate, the muzzle treatment, etc, would give me a better chance to comment.