It is difficult to say whether or not your son has been identified by the police or not. I tend to agree that with eight weeks having gone by it would seem unlikely. However, the delay might also simply be the result of the police being otherwise occupied with other more pressing matters; therefore, I unfortunately can not tell you of a specific period of time that once it has elapsed your son can consider himself in the clear. There is no practical way that you can reimburse the city for the damages without the city knowing who the money came from, or what it is for. Even worse would be if you simply were to drop off an envelope with cash and then your son gets charged; how would you ever prove that that money for restitution came from you. You and your son could very well end up paying the restitution twice. I think the best course of action is simply to not do anything; set the money aside for the restitution if and when anything should ever happen. The only other real course of action you can take if you really want finality to this matter is simply to get your son an attorney and make arrangements to get this matter cleared up with the authorities. It is not inconceivable that this matter might get resolved without anything formally taking place in the courts.