What does Slim do with the newborn puppies?

Give them to Lennie. George approved of Slim giving the puppies to Lennie. He had to approve this, because he is Lennie's caretaker. He takes care of him because Lennie is mentally handicapped, which makes him forgetful and often times make decisions that get the two of them in trouble.

The puppies were a win-win for everyone involved. Slim was able to easily get rid of them to George and Lennie. For Lennie, the puppies were to give him a source of companionship. For George, he hoped that Lennie having the puppies would keep him out of trouble.