Step 1 after placing the stone in the book there should be an option to give it to him... Assuming he is around and you didn't already give it to some one else
Step 2, select gale as your character and open the book from his inventory ie right click and use
Then pass the tests and he gets a new spell
Doesn't work that way if I remember correctly. Gale does not get the book same as Astarion after you choose the option. He also does not need to read the book, he needs to consume its magic. And this is done by long resting (can take several rests) and triggering his particular scene.
