Is there repentance for a man who falsely accused his wife of adultery and then regretted it, or has he fallen from God's mercy?

If a man accuses his wife of adultery without proof, he has committed a grave sin and a major transgression. He must repent sincerely by abandoning the sin, regretting his action, resolving not to return to it, seeking his wife's forgiveness for the injustice, and informing those who heard him that he was untruthful in his accusation. He should also increase his good deeds, seek forgiveness, and supplicate frequently.