Although I can’t make a diagnosis on the basis of a short letter, what you are describing is consistent with someone who is significantly depressed. Although the loss of his girlfriend didn’t help matters, I don’t think that is the root of the problem. It is even possible that his depressed mood contributed to the break up. I can’t know without talking to him. I also can’t comment on whether his mother’s death contributes to his problem. That would depend on his relationship with her and how he and his mother handled her illness.
Your friend is very fortunate to have such caring friends. Unfortunately, there isn’t much you can do beyond what you are already doing — talking to him and encouraging him to get into treatment. His father might have more leverage since your friend is living with him. His father could confer with a therapist about how best to help him and then try to involve his son.
Treatment does work. Studies show that 75% of people who enter therapy do benefit. But therapy only works if the patient engages. You can’t do that for him.
I wish you well.