Right, so wizards can use it to learn a spell.
What does that mean?
  • All uses of "learns a new spell" in the wizard entry refer to writing it in the book, so this feat would probably do that.
  • Thus they can't write it from memory.

You use the feat to write the spell down in your book. If that book is gone, you lost that copy of the spell. If you don't have another copy, you don't have that spell anymore.