There is no 'FL' region for the purposes of precious metal marking in Italy. Your mark image is not clear, but I suspect it may be '336 FI', if that is the case, then your photoframe is the work of Paterna & Livi.
The top is not solid silver as such, but a resin base covered with a layer of silver. To identify such pieces and so that they are not to be confused with solid silver items, as they do contain a full set of Italian marks, the Italian government required some extra marks to be struck. These extra marks are a 'R' within a square, this stands for 'Riempito' (filled), and also a set of figures that indicate the amount of silver applied, in grams (1÷2 g, 2÷3 g, 3÷5g, etc.). These are not exact weights, but must fit into range stated by each mark, in this case, between 10 and 13 grams are applied.
I've just noticed the third mark from the left, it is the trade mark of Paterna & Livi.