That Moiraine was pretty good at figuring out Forsaken. She also quickly found out who Sammael and Be'lal were, since she apparently knew quite a lot about the Forsaken (she reads a book about them in TGH).

As the others said, she certainly eavesdropped on Rand and Asmo's conversations and thus figured that Jasin must be a male Forsaken, namely most likely Asmodean (except for LTT's arch enemy Demandred and Asmo all male Forsaken were dead at this time, or it was known where they stayed ).

Besides that, in TSR, ch.52, Birgitte tells Nynaeve that Asmo is at Rhuidean in the waste. Nynaeve considers then that she has to warn Egwene at their mext meeting in TAR during the next days. Probably that happened of-screen and Moiraine also learned about this from Egwene. Another piece of the puzzle.