The part is not original (in the sense of "as when first sold"). Originally, the cup was made of sheet metal and the lower metal part could be unscrewed. The insulating body was made of glass mirrored on the inside and the cap was made of cork. We disposed of our bottle after the lower glass tip broke off during (somewhat careless) cleaning. Then the insulating effect was gone.
The bottle was from the early 50s.

According to the information found, yes.