Deer Kees Van den Heuvel,
Searching through the internet I stumbled upon your article of 2013 about Capt. Thomas Moore of HMS Fame of Dublin. My friend from Limerick, Ireland is writing a paper about her trying to find any information on Fame Privateer of Dublin under the command of Mr. Thomas Moore. In particular, he found out the Fame was sold in July 1782 to a firm called Chiocchini & Strambi of Livorno. He says that Fame may have been working under contract for the Russian government. She may very well have been renamed the Saint Peter for less than three years later a vessel pertaining to this company sailing under a Russian flag, sunk off Holland around December 1785, causing great distress to merchants in Livorno.
Myself have been looking it up in the Russian archives of the XVIII century but all in vain. If you know anything about what finally happened to this ship Fame, we would be very appreciated.