Praise be to Allah.
What you must do is be patient until the owner of the watch comes and gives you what he owes to you. If that is too difficult for you and you do not want to wait, then you can sell it by auction in the marketplace for the best price, then take what is owed to you and keep the rest for its owner. Then if he comes to you some day, you can give him his due. If a long time goes by and you do not know him and you are not able to give him his due, then you can give it in charity to the poor, with the intention of that being on behalf of the owner. This is the way prescribed in Islamic teachings for dealing with this matter. End quote.
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him).
Fataawa Noor ‘ala ad-Darb, 3/1457.