That's an interesting way of thinking about it. My take on it is the opposite. If an accurate copy of me was made after my death, I am pretty sure the copy wouldn't care if it was me or not, just as I don't care if I am as my past self wished me to be. If the copy was convinced it was me, there would be no problem. If it was convinced it wasn't, than it wouldn't think of my death as any more important than the deaths of everyone else throughout history.