How did Sir Simon come to rest?

There is a prophecy written on the library window which, Sir Simon believes, is a reference to Virginia and the manner in which she will help him cross over to the other side. According to the prophecy, "peace [will] come to Canterville" when that "golden girl" intercedes for Sir Simon and enables him to cross over, despite his lack of faith. Simon tells Virginia that she needs to weep with him and then pray for his soul so that the angel of death will take pity on Sir Simon, despite the fact that he himself has no faith. He is sure that the "purity of a little child" will be sufficient to sway the powers that be and allow him finally to sleep. Simon is extremely tired and has been unable to sleep for over three hundred years, longing for the Garden of Death, in which he would be at peace.
In answer to Simon's plea, Virginia tells him that she is not frightened of him and that she will certainly pray for him and his soul. When she begins to do so, the embroidered men on the tapestry in the room implore her to retreat, but she only clings more tightly to Simon's hand, and she is rewarded for her bravery. When she and Simon reach the other side of the room, he is subsumed by a "great black cavern," which leaves the room empty. Virginia then recognizes that Simon has passed over and is finally at peace due to her bravery, purity, and faith.

Sir Simon has been haunting Canterville Hall for centuries as the punishment for murdering his wife. He is tired of being a ghost, but since he has no faith, he can't pray to be delivered. He needs someone pure and faithful to do this for him. However, people have been afraid of him because he is a ghost, so he hasn't been able to communicate his need. The Otises are not fearful of him but so far have mostly tormented him.
One day, Virginia Otis, who is pure and compassionate, comes across Sir Simon and realizes he is unhappy. He confides to her that he would like to go to his final rest in the grave but can't without her help. She agrees to pray and intercede on his behalf. She does so, and finally, his body dies for good and can be buried. He has achieved his final rest through her kindness.