I'm hoping it's just the difficulties of accurately expressing tone via social media that are making you sound so calm and unperturbed. If not, you need to find some white hot anger and true disgust at your son's actions.
I went to school with a lad who hung himself after being bullied. He couldn't take it any more. The consequences of the behaviour of children like your son can be devastating and span generations. That poor boy will never grow up, have a family and a career. His parents will never get over it. His siblings will always miss him.
The immediate concern for me is the victim's wellbeing. I know school is closed, but are you able to contact his parents over social media to let them know what's happened so they can support their traumatised child? If not, you need to be on the phone as soon as school opens on Monday to ensure that this child is being supported and checked on.
Then there's the issue of how you deal with the bully. It sounds like his friendship group is a huge catalyst for his behaviour given that he seems to be enjoying bragging rights. Either he is desperate to fit in with that particular group, or he feels pressured to behave a certain way, or he is "leader of the pack" and is flexing and enjoying all the attention and kudos. Whatever the reason, I would be immediately and permanently severing those ties. Those friendships would no longer be permitted and I would be demanding that school get on board by taking immediate steps to disband this toxic group for their own sakes and for the safety of other pupils (separating them in lessons and monitoring to ensure they remain separated at break times - spending their break times in detention if they won't remain apart). At home, I would be ensuring that DS had no means of contacting them at all. No phone, no tablet/laptop/PC, no Xbox. Nothing. This wouldn't be "I'm taking away your phone for a week". For me, I'd be taking it all away indefinitely with no current plans to return it. Buy an alarm clock so he has absolutely no excuse to need his phone.
He would be going to school and coming home. No playing out or leaving the house without a parent. At home I would allow access to wholesome and valuable pastimes such as reading, art materials, writing materials etc but no electronics whatsoever. If a laptop is required for school work, he would be doing it in a public part of the house (which is where all children should be if they are online anyway) and I would literally be hovering over him or sat right next to him to supervise his internet use.
I would be handing his freshly laundered blazer into the school office so that the other boy could take it (if he wants to) to use until DS has earned enough money to pay for a new one for the child.
I would demand that he write proper, meaningful apology letters to the boy and his parents. I would get the headteacher to offer the boy and his parents the opportunity to recieve a face to face apology (bear in mind they may not want to).
Given that this is now a pattern of behaviour for your son and not an isolated or out of character incident, you need to come down extremely heavily. His behaviour could quite literally drive another child to suicide. It's that serious. You need to take drastic steps.