Just trying to understand exactly what steps you followed here.
If you give Gale the book in dialogue after putting the gem into it, then in my experience it vanishes from his inventory but next long rest there’s a cutscene which shows him consuming it. If he still needs an item, anyway.
If you put the book in Gale’s inventory and have him trigger the cutscene to open and read the book, then it stays in his inventory and he won’t treat it as an item he can consume which I admit is a bit odd. Is this the scenario you’ve come across? I
posted some info about what happened with Gale’s personal quest when I tried this in my patch 9 playthrough on this forum, but sounds like you might have done things in a different order as he didn’t ask for the book, though he did request other magical items later.