No amount of extra protein will speed the growth process. Boys generally grow fastest between the ages of 13 and 14. This growth spurt lasts longer in boys than in girls, and after the growth spurt boys continue to grow slowly until about age 20. My 11 year old son wants to start lifting weights to bulk up. But it will not contribute to bulkier muscles until he has enough male hormones to support muscular development.
Boys bulk up after they have finished their growth spurt.
Remind him that patience is a virtue. Muscles do not turn to fat, nor does fat turn into muscle. They are two separate entities and are not interchangeable. Perhaps you have noticed a fat layer on roast beef or pork chops. A similar fat layer occurs with humans.