I do not believe there was ever a “Martini-Henry” patent as such.

When the British Government adopted the new rifle using the Matini Patent action it was decided to rifle the barrels with Henry Patent rifling.

The resulting rifle thus being known as the Martini-Henry.

The neat little .44-40 Reilly rifle you show is clearly a Martini. It should only be described as a “Martini-Henry” if it has Henry’s rifling.