I figure a fair amount of modern heritable information (such as morals) will not be lost. Civilization seems to be getting better at keeping and passing on records. You pretty-much have to hypothesize a breakdown of civilization for much of genuine value to be lost - an unprecedented and unlikely phenomenon.

However, I expect increasing amounts of it to be preserved mostly in history books and museums as time passes. Over time, that will probably include most DNA-based creatures - including humans.

Evolution is rather like a rope. Just as no strand in a rope goes from one end to the other, most genes don't tend to do that either. That doesn't mean the rope is weak, or that future creatures are not - partly - our descendants.