Yadirf:
You asked: Why, may I ask, are you inclined towards thinking that there must be "continuity" in order for the person who is restored to life to be the "same" person who died.
Because without some continuity nothing is "the same." If you completely incinerate a piece of glazed clay pottery to the point that absolutely not one particle of it remains, and then create with all new clay and glazing a new piece of glazed clay pottery exactly like the old object that no longer existed, is that new piece of pottery the "same" piece of pottery that was completely incinerated? No, it is not. It is just a copy of that piece of pottery. On the other hand, if only a small part of that piece of glazed clay pottery, say for instance its glazing, is lost due to wear but is later restored, then it can truthfully be said that the reglazed piece of pottery is "the same" piece of pottery as the old piece of pottery. Why? Because the most important part of the piece of pottery never ceased to exist and remains under its new glazing.
It is theoretically possible for DNA from a dead person to be used to create a living clone of that dead person. The clone will then be a perfect replica of the dead person. But it will not be the dead person. It will only be a clone, a copy. Why will it not be the dead person? Because no continuity exists between the dead person and the clone.