Our only direct evidence comes from a note reproduced in Unfinished Tales regarding Morwen Steelsheen, a lady of Gondor who became queen to Thengel of Rohan (and was thus Théoden's mother). This note tells us that her father came originally '...from Belfalas; he was a descendant of a former Prince of that fief, and thus a kinsman of Prince Imrahil.' (Unfinished Tales of Númenor and Middle-earth, Part Three I, The Disaster of the Gladden Fields, Appendix).

This establishes that there were at one time Princes of Belfalas, and the reference to Imrahil shows that they were related to the Princes of Dol Amroth. These were presumably the people of Imrazör, descending from a line of Númenóreans who settled in Gondor independently of Elendil and his sons.

It is unclear what became of the Princes of Belfalas, but the simplest explanation is that, when Galador established his seat at Dol Amroth (which only received its name at this point in history) the line simply continued under the new style of the Princes of Dol Amroth.