can reksai trigger her legend ability if she moves onto forgotten monument turn two?

No. Moving onto Forgotten Monument on your second turn doesn't produce a Conquer, so Rek'Sai's "When you conquer" trigger never fires.

Forgotten Monument says "Players can't score here until their third turn," and Conquer is a method of Scoring (CR 471.1). Before your third turn, the entire scoring action — including the Conquer itself — is prevented (FAQ #9332). You can still move a unit there and establish control, but since no Conquer occurs, Rek'Sai (Void Burrower) has nothing to trigger on. On your third turn, though, the restriction lifts and the move will conquer normally, triggering her ability.