Is it permissible for the wronged person to say to the one who wronged him: "I do not want money, but I pray to God that he will have fire in the Hereafter"?

It is permissible for the oppressed to supplicate against their oppressor with the aforementioned supplication, whether they confront them with it or not. However, forgiveness and pardon are more virtuous, for Allah Almighty says: "So whoever pardons and makes reconciliation - his reward is due from Allah."