Oh yeah, all the basic stuff is no problem to remember from one life to the next. The strongest memories are the ones you think about pretty often, and you talk and read and write and do basic math all the time.
Typically skills and memories do fade, though. And dexterity based skills can be lost in a single lifetime. Muscle memory doesn’t transfer, so if you were really good at some reflex based sport or something, you’ll lose a lot of that going from one life to the next.
In terms of mental skills though, it’s also true. If you learn some technical profession, then you don’t practice it for a few lives, you’re going to be really rusty by the time you try it again, and probably have to refresh a lot it in your mind.