All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
Such a relationship as the one between that girl and that young man is not permissible, nor is their chatting on the Internet and through other means, as they are non-Mahram (marriageable kin) to each other. Please refer to fatwas 84079 and 81356. She should be advised to repent to Allah from this relationship. If marriage is facilitated between her and that man afterwards, then that is fine; otherwise, each of them should go their separate ways.
It is a sign of good manners that that young man acknowledges the kindness that he received from the other man and wishes to return the favor and reward him; this is indeed the conduct of noble people.
It is for this reason that Allah Almighty, the Most Generous and the Most Kind, rewards good for good; Allah says (what means): {Is the reward for good [anything] but good?} [Quran 50:60]
This is also one of the traits of the Prophet . Jubayr ibn Mut’im narrated that the Prophet said concerning the prisoners taken in the Battle of Badr, “If Al-Mut’im ibn ’Adiyy had been alive and had spoken to me about those filthy ones (as they were polytheists), I would have freed them for him.” [Al-Bukhaari]
Al-Mut’im was among those who sought to override the injustice of Quraysh, and when the Prophet returned from Taa'if, Al-Mut’am sheltered him under his protection.
However, the person whom you mentioned is not obliged to reward the other man by marrying his daughter. If his marriage to her is facilitated, then that is fine; otherwise he may recompense that man by anything else, among which is to supplicate for him with goodness as much as is possible.
‘Abdullah ibn ‘Umar narrated that the Prophet said, “Grant shelter to the one who asks for it in the Name of Allah; give to the one who begs in the Name of Allah; accept the invitation of the one who invites you; and requite the one who does a favor to you; but if you are unable to requite him, then continue supplicating for him till you feel that you have requited him adequately.” [Ahmad, Abu Daawood, and An-Nasaa’i]
He may also supplicate Allah to rectify her and ask Him to make her his wife if this is good for him.
Finally, it should be mentioned that if someone already proposed to that girl and she accepted him, it is not permissible for that man to ask her for marriage as she was approached for marriage beforehand by another man, even if his intention is to reward her father.
Allah knows best.