What is the religious ruling on falling in love with a girl online, and the resulting attachment and correspondence, and is abandoning her considered an injustice that necessitates not forgiving?

Speech and correspondence between young men and women who are not mahrams is a gateway to fitna (temptation, discord) and a means to corruption and evil. Therefore, you must repent to Allah and cut off your relationship with them. If you are able to marry the girl you have become attached to, there is no objection, and what is considered in the compatibility between spouses is religiosity. However, if you are unable to marry her, then you must turn away from her and occupy yourself with what benefits you in your religion and your worldly life.