If humanity were to become extinct, do you think another animal species would evolve to take our place? What lessons do you think they'd learn from our successes and failures?
If humanity were to become extinct, I'm fairly convinced no other animal species would evolve to take our place. There are literally millions of things that have to happen in order to create a species that is both intelligent and driven enough to change its environment in the way we have, and humans are full of so many unique biological quirks that I can't see any other species filling that role. Even something as small as an estrus cycle vs. a menstrual cycle changes the ballgame completely.
In the unlikely event that another species did rise up eons down the road, humans won't even have been remembered to exist. They would learn nothing from something of which that they have no concept.