How did Faramir know?

[Lord of Angmar]

Maybe it was because he did heal him and maybe Faramir knew that the heir of Isildur had healing powers.

I agree, Gorwingel. In the book it says something along the lines of, "the hand of the King is the hand of the Healer" (I would provide the exact quote if I had a copy of RotK available). As a Son of Gondor and a Captain of her army, I am sure Faramir would know this quite well, and also perhaps his "Elvish" senses detected an aura of a man of the line of Elendil.