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

Luke Skywalker: I don't, I don't believe it.
Yoda: That is why you failed.