My son is six. We read a picture book everyday and he is starting to read on his own a bit, too.
Unless we keep every book we have read and maybe as a teenager, he might find the box of children's books in the attic and then remind himself of all the books we have read...But there's no way he could recall all the books we read last week even without some help.
Or, since he will probably read his first long novel soon, I bet he will always remember what his first long chapter book was. He likes to read and that would be an accomplishment he will remember.
Oh, and as his mom, if I remembered what novels he read, and reminded him throughout his childhood, then he would be more likely to remember when he is 15. (I'm thinking, like, if he's having a hard time in school one year, I could remind him, "You are so bright. Don't you remember you read Charlotte's Web all by yourself when you were 6? And all the Magic Tree House books, too..." if that was part of my normal pep talk, it would be engrained in his memory.
Does that info work with the story you are writing?