I was researching on an unrelated topic when I came across this piece of information on The Thain’s Book (www.tuckbourough.net).
It concerns Aragorn’s claim to the throne of Gondor. In this essay the author seems to imply that the heirs of Anarion, King of Gondor died out, and that Aragorn therefore claimed it as the closest relative. However, The Thain’s Book, under the entry Firiel, clearly states that it did not. Rather this entry states that Firiel who was of Anarion’s line, married Arvedui, the last King of Arthedain (all that was left of Arnor). Thus Aragorn Arathornion was not only the heir of Isildur, but also the heir of Anarion. This explains why even though there was a legitimate Steward (Faramir), the rule of Gondor passed to Aragorn, because Aragorn actually had the better claim, because despite the fact that the Council of Gondor had refuted Arvedui’s claim after the death of Firiel’s brothers, he was still the blood heir, and the only remaining descendent. If Aragorn had not also been Anarion’s heir he could not have legitimately claimed Gondor without first disposing of Faramir, because the claim of a Steward, seemingly trumps the claim of Isildur’s heir (otherwise the Kings of Arthedain would have claimed Gondor). Tolkien mentions no such fight between Aragorn and Faramir, nor does he show any sign of tension between those two. Thus I must conclude that Aragorn was accepted as Anarion’s heir as well, perhaps they considered it legitimate for Aragorn to claim Gondor since he was Firiel’s descendent and not simply her husband?. I am not sure.
This information is given on The Thain’s Book as coming from Appendix A of The Lord of the Rings pgs.321-23 “The North-Kingdom and the Dunedain” and pgs.329-30 “Gondor and the Heirs of Anarion”. However I have not actually checked the Appendix myself.