How can one be absolved from wronging a girl who was defrauded through identity theft, and avoid Allah's torment and the pangs of conscience?

Islam has forbidden any relationship between a man and an unrelated woman, to block the means to temptation and to protect society from vice, as Allah Almighty said: "not unlawfully carnally knowledgeable, nor taking them as secret lovers." You were right to cut off your relationship with her, and you must fulfill the conditions of repentance. You are not required to tell her the truth or to ask for her forgiveness; rather, it is sufficient to supplicate for her well-being.