While I have no doubt that is an absolutely minty officers tschapka and a very nice carrying case I would hesitate to believe that is the actual Duke's helmet.
All of the attributed royalty and/or titled owner helmets I have seen, have had the owners monogram in the silk lining. Whether it was a gold stamp or actual metal insignia there was always something that identified the owner.
Unless there was a rock solid provenance, a paper label with a Duke's name on it doesn't cut the mustard to me.
Remember, buy the helmet...not the story. That's a lot of bones for a Officer's helmet and a pretty case.
John