In plain words
Hanumān, when she asks how he knows: Vaidēhī, whose kohl-dark hair is fit for fine flowers, hear a plea: as the king of the monkeys [Sugrīva], famed for sharing his joys and griefs, stayed with him to search for you, the king of the people of Ayōdhyā, whose good qualities befit that state [of separation from you], told me these tokens. This is how the tokens came to me; and this is the ring from his own hand.