What is the ruling on abandoning a woman after having an illicit relationship with her, or on first inviting her to Islam and then leaving her, knowing that the probability of her embracing Islam is high?

Strive in inviting the non-Muslim woman to Islam through righteous women or Islamic centers. If she embraces Islam and becomes steadfast, one may marry her if there is a desire to do so; otherwise, she must be left alone. This should be coupled with sincere repentance and abundant good deeds.