[William Cloud Hicklin]

Certainly, Aragorn, during his first 50 years prior to meeting Arwen in Lorien the second time, must have spent time in Dol Amroth, visiting and looking about, and perhaps making renown enough for himself, that he could pull a favour from Imrahil more easily. As far as Dol Amroth was concerned, a very long time ago, Isildur's and Anarion's line vanished. I wonder how 'lore wise' Imrahil actually was in his Princedom. As someone of such prominence in Gondor in a legitimate Princedom, he was not going to easily take orders from Aragorn, or, not lightly, accept the claim Aragorn Made. I suspect Aragorn fostered relations and got renown for himself (as noted in Tale of Aragorn and Arwen, though they did not mention 'exactly where' he got his reputation).

Except for that theory to hold up, Imrahil would somehow have to have found out that Aragorn was the same as the 'Thorongil' of his boyhood.