The only "official statement" concerning the succession was Michael's to Frankie in the boathouse: "Clemenza promist the Rosato brothers three territories in the Bronx after he died... You didn't give them to him." The only thing we can be sure of is that this tells us for sure is that Frankie was Clemenza's successor--probably (but not necessarily certainly) his immediate successor. We know nothing for sure about what Frankie did under Clemenza, or how he came to be Clemenza's successor.
We also can be sure that either Frankie or the Rosato Brothers are mediums who can communicate with the dead (i.e., "Clemenza promised ... after he died."
