Is that eau d'cod wafting around this page?
Could it be that the alleged muggng is a line he's spun granny because he lost or broke his watch through carelessness or sold it for a pittance/gave it to a friend/was bullied out of it?
This might explain his desire for the police not to be involved, but why would granny go along with him? Are the police to be feared if you become a victim of crime?
It seems to me that more details from granny are needed as to exactly what he told her before you sit down with him and attempt to get to the truth of the matter.
As for the £85 watch, that gets put away for high days and holidays and you take him out to choose a cheapy for everyday use. Politely tell Granny that any gift with a value of more than £5 needs to be cleared with you before she gives it to him, and that expensive presents are to be reserved for special occasions such as Christmas, birthdays etc.
You have my sympathy, but so does he as he's being required to adjust to a new family structure in a new environment miles away from the one constant in his life, and to comply with a different set of rules and expectations of behaviour - that's not easy at any age but it can be particularly difficult for young teenagers.
Don't expect miracles; progress will be incremental and sometimes it may seem as if it's one step forward and two back but that's entirely normal in these situations.
Be kind to yourself, and to him, and to poor Granny who's likely to be consumed with guilt and full of regret for the loss of her child and her grandchild.