Caring about what happens after you die

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?