A Royal Oak's reference and configuration can identify a model. They don't tell you whether the individual watch has a theft report. For that, ask for the serial on the actual piece.
Match the number before you search
Compare the engraving with the seller's invoice, warranty papers, and service documents. If the case hides the number, let a qualified watchmaker inspect it. A serial typed in a message is not yet connected to the watch in the listing.
Use a dated search
Search the verified serial and save the result. A match calls for a pause and follow-up with the provider. No match means no report was found in the searched data at that time; it doesn't establish title or authenticity.
Review the whole transaction
Ask who is selling the watch and what records support that sale. Put the serial, price, and condition on the invoice. If the number differs anywhere, resolve that before transferring funds.
Check the Royal Oak Serial
Confirm the number belongs to the physical watch and compare it with the paperwork.