Unfortunate plot hole
I enjoyed the movie, but there is a plot hole that can not be overlooked. People have mentioned the lack of research into the family, but there is one even bigger one than that. At the level of art and antiques that Oldman auctioned, provenance is everything. It would have been immediately apparent that fake Claire knew nothing about the furnishings, or that the stories about the furniture and paintings didn't add up, as real Claire said that they were carried in. Any existing furnishings would have been real Claire's. and fake Claire wouldn't have known their story either. Even if Oldman could have identified most of the furnishings stylisticaly, he would have been extremely suspicious of a palazzo of art and furniture without provenance, and the value would have been substantially under market.
Obviously filmed in Italy, every Italian noble family I know can identify 90% of everything in their home, even if this is an English or Danish noble family in Italy. "This was a gift from the Principessa Borghessi. We received that from his holiness Pio IX".
I did also have trouble with the English in what was obviously an Italian setting. I would not have hurt for the bar scenes to have been in Italian with sub-titles.