What is to be done concerning a man who stipulated in his will that he be buried in the mosque he built and was buried in?

This will is invalid and contrary to Islamic law, for a mosque and a grave can never coexist in Islam. The ruling goes to whichever came first. Since the mosque was built first, the grave must be exhumed and removed from the mosque, and the deceased should be buried with Muslims in the graveyards, as the Prophet (peace be upon him) forbade taking graves as places of worship.