If an Old Believer is received into the Catholic Church, are they automatically ascribed to an Eastern Church sui juris, even if they are received in a Roman parish? I know this is the case for Orthodox Christians who are received into the Church, and it seems that it might be the same for Old Believers, but I can't find any info on that.
Since the Old Believers are a schism from the Russian Orthodox Church, it would make sense for an Old Believer to be ascribed to the Russian Catholic Church. Historically, the Russian Greek Catholic Church had Old Believer parishes (there is a fascinating thread here on the forum about Catholic Old Believers.).
Unfortunately there is no hierarchy of the RGCC other than the local Latin hierarchy so anything "official" becomes more complicated. We have several in Ukraine who went to the UGCC, and if memory serves me correctly we have one of those as a Studite monk in Univ or one of its sketes.