From sometime in later 1940 until the end of Ssh39 production, LMZ helmets had a high degree of standardization. With the small number being made with no sweatband being the one curious exception, they should all follow a certain theme. This one does not. Looks like a relined original shell to me. The pictures are not very good, but the stamp looks like an original, early (1940 dated) example of the final LMZ stamp found in Ssh39.
I wish there were better pictures of the star. Possibly the fresh appearance throws up a flag for you and this is certainly wise. However, for an LMZ factory applied star, it appears this one is in the typical position and the paint has a thickness that is expected on such a factory application.
In the end and based on these photos, I think this helmet has a reproduction (fake) liner and a replaced chinstrap. Possibly a complete rebuild, as the rivets seem to be "unusual"