Whether a person’s influence “lives on” in their children, or in the world in general, is of no concern to me if I’m not there to witness it! There is no world unless the “I” is present to observe it! Everything else is just some kind of pipe dream that an ego, which expects its own extinction upon bodily death, holds onto! And it's a kind of "afterlife" that is of no interest to me, whatsoever!
As far as I'm concerned, if a person doesn't live on as a conscious being then they don't live on at all. Other people's memories and experiences belong to them, not oneself! And when (or more accurately, if) one's consciousness ceases to function, then for the "I" nothing effectively exists!