Behaviour like your son's is what drives people to self harming and suicide, and I honestly think that is what you need to drive home. If a child he bullied did go that far, I would drag him to the funeral and make him stand face to face with what he had done. People like your son only learn through the harshest ways. When I was a teen, a boy was bullying me on a daily basis through tactics like what your son implements and verbal. I had rotten food thrown on me and smeared into my long hair, clothes ripped off me, pushed, kicked, called a bitch and worst of all, I was laughed at because my Dad had died. I was told nearly daily to go and cut myself on my Dad's grave and kill myself. If you don't stop your son, it will escalate to behaviour like this. In the end, I had a mental breakdown at the age of 13/14 and had to leave school. It severely fucked up the quality of my education, my confidence and my mental health. All my friends deserted me. I left school with 1 qualification, and worst of all, I was so messed up by the ordeal I found it hard to eat and as a result nearly died from undereating. At 30 years old, I still think about it and get upset, sometimes I have nightmares about it and other times I think about going back in time and standing up for myself and beating the shit out of the little rat bastard. Your son needs to learn empathy, and pretty fucking quickly, or else who knows where he'll end up. What if he turns it towards women? What if he picks on the wrong lad and they lay him out flat and he ends up in hospital? I don't mean to cast judgement, but he sounds like a psychopath, the fact he's tried to manipulate the situation to sound like the other child was 'crazy'. Been there, done that. He needs harsh intervention and this instant. His behaviour is beyond disgusting and abhorrent.
Take away his phone. He's no longer allowed one until he can afford it.
No video games, because why should he deserve pleasure while another child is probably going through mental anguish at what has happened?
Talk to him THOROUGHLY about the fact that him being so disgusting to another child could cause them to end their life. That if that were to happen, you would force him to the funeral to fully absorb the consequences of his actions. Watch videos of people he admires (youtubers/celebs etc)talking about suicide and bullying.
Flip it on it's head - tell him to really think about how he would feel if he was the one getting dunked on. Or if he has siblings, what if it was them?
No socialising with the lads he has been gloating with. They are obviously the same.
Get him enlisted with the local Army Cadets if you have one local to you. It might give him a sense of purpose other than making other children's lives misery and being surrounded by nicer people might have a positive influence on him.
No Christmas. Sorry, but this type of behaviour doesn't deserve to be rewarded, especially so close to Christmas. Might be harsh, but that's what you get when you act an absolute fool.
I might sound angry and bitter, because yeah, I am. Children like yours ruined my best years and I am only just getting through it now, but he needs to learn before he ruins someone else's life or has his own messed up by picking on the wrong person.
Just food for thought.