You cannot make such AGI if the information is gone. Imaging & cryopreservation sort of insure against early death.

I agree that at point behavioural replication is possible, AI probably also will be. Harsh.

Now the point you ended your reply in is a very common response. Many follow the same direction of thought. I think that to think one should not get a behavioural replica because you don't think it would be you is a non-sequitur however; if the behavioural replica continues to advance your interests, is it not the rational thing to do?

Moreover, if you said "no, it doesnt matter, I'll be dead" you would be following a strategy that'd lead to huge loss if it turned out you actually never died.