Yes, the short form is 'll -- I'll, you'll, he'll, and so on.
Sometimes, though, the short form would be too difficult to pronounce: "William'll be king one day" is almost impossible. Better to say: "William will be king one day".
There used to be a children's TV show in Britain. Children would write in asking the host, Jimmy Saville, if he could "fix it" for them to do something. For example, somebody might write in and say, "Could you fix it for me to see the Rolls Royce factory", and Jim would arrange for them to visit the factory and see how Rolls Royce cars are made.