Easier said then done
The watch industry is not nearly as tech savvy as you'd like, something to do with selling obsolete tech. Even assuming that he reported the watch stolen to IWC, which not many people do, unless the Jeweler was an authorized dealer, it's unlikely they'd have even responded to his queries and neigh impossible that it would have happened in a timely manner. The jeweler probably made a copy of his drivers license and simply passed that on to the copy when questioned