I think I remember reading another sci-fi book or short story that posited the classic "teleporter problem" but the device functioned by making a copy of the in

I think I remember reading another sci-fi book or short story that posited the classic "teleporter problem" but the device functioned by making a copy of the individual and then destroying the original, similar to The Prestige I suppose. Part of the plot centered around the original escaping that fate and then fighting for their continued existence. I think it poses a very strong argument against a copy of consciousness being a continuation since it makes no sense that there is continuity between copy and original only if the original is immediately destroyed, it just means that the copy is the only remaining instance.