He is prohibited from regurgitating source material, of course! But if he generalized from the books he read and really learned the subject--and even made new connections between ideas--then he is free to write his own book.

He is not prohibited from "regurgitating source material" in many cases. Facts are free. It doesn't matter who first measured Young's Modulus of aluminum, anyone may state that fact as originally presented.

The professor is free to lift all the facts and formula they want. They just need to rephrase explanations. Which is pretty much what an LLM is going to do.