Is the above-mentioned a quest item book? My brother has picked it up and cannot drop it... but I don't remember anyone asking for the book...

I think It's a book Urag at the college asks for in a book retrieval quest

Good luck, unless you are on PC you'll have that book in your inventory "ad eternam".

Mine was a quest item until I continued the MQ a little bit further, but it's the only copy in the game I think, so you should keep it if you're into collecting rare books.

I did the MQ earlier today. This book is presented by Esbern, when you pick him up in Riften and return with him and Delphine to Riverwood.

This... he was able to put it down after progressing a little further (and doing Alduin's Wall). Cheers.