He writes in the book is perfectly correct - you don't need to be in the book to use it. (If you were in the book like the neverending story and meant it that way you'd need to clarify.) In the original sentence "in" is used to mean inside - but a native speaker would use the first sentence as it is. He writes into the book sounds clumsy or uncommon to me. (I am a native speaker)
Judging by your comments, I would say that he speaks far better English than you do. Try the English tree, it might help you. By the way, "your" = 2nd person possessive (il tuo/la tua), "you're" = contraction of "you are" (tu sei). And "I don't even know what that" is nonsense, maybe you forgot to finish the sentence. Hope that helps, good luck.
THIS IS STUPID IF I WAS TRAVELING TO ITALY I WOULD NEED TO KNOW "WHERE IS THE WASHROOM" OR "PASS THE BREAD PLEASE" NOT "HE WRITES IN THE BOOK!!!! ITS ALSO GRAMMATICALLY AWKWARD! I WOULD NEVER SAY THAT AND I HATE THIS! ALSO I"M COOLER THAN THAN THE MOON, I JUST THOUGHT I'D TELL YOU!!