He is not allowed to give any memory to someone, but every time Gabriel wakes up at night Jonas chooses to give memories expecting him to relax and go to sleep, but even though he does that, I do not think its the best way to calm the baby because he is breaking a very important rule from his job.
He received the giver's favourite memory which was the Christmass memory. This experience helped Jonas understand love, union, happiness and many more beautiful feelings when you are with your family. Jonas is learning more about the "Elsewhere" which I think is the normal world. So maybe having this memories will want him to escape and feel it by himself by being in the normal world. WE WILL SEE WHAT HAPPENS!