Usually when you add a named driver you are asked if they have access to another car, if they have had any claims and/or convictions in the last two years. You must answer these questions truthfully. They may ask what the claim was for, and as it was for something stolen from the car, rather than an accident, I doubt your payments will go up. If you answer the questions fraudulently then they are more than likely to not cover your son if he attempts to make a claim in your car.