This seems isomorphic to the mainstream debate, in academic philosophy, over whether one can be harmed by things happening after one's death; in other words, precisely how do one's preferences (for certain states of affairs) after one's death work?
See: http://plato.stanford.edu/entries/death/
"Third, what is the case for and the case against the harm thesis, the claim that death can harm the individual who dies, and the posthumous harm thesis, according to which events that occur after an individual dies can still harm that individual?"
Hm. I think worrying about whether something can "harm" a dead person carries much more semantic baggage, so the key ideas will probably be different.
More than once, I've had a conversation roughly similar to the following:
Me: "I want to live forever, of course; but even if I don't, I'd still like for some sort of sapience to keep on living."
Someone else: "Yeah, so? You'll be dead, so how/why should you care?"
I've tried describing how it's the me-of-the-present who's caring about which sort of future comes to pass, but I haven't been able to do so in a way that doesn't fall flat. Might you have any thoughts on how to better frame this idea?