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, sallallahu ʻalayhi wa sallam, is His slave and Messenger.
There is no doubt that a love affair outside of marriage is prohibited in Islamic Shariah. Rather, it is one of the practices of the Jaahiliyyah (pre-Islamic period of ignorance) which Islam abolished. Allah, the Exalted, says (what means): {(They should be) chaste, neither of those who commit unlawful intercourse randomly nor those who take (secret) lovers.} [Quran 4:25] Hence, it is incumbent on this young man and woman to repent to Allah of their illegitimate relationship.
As for her marriage to this young man, if his religiosity and manners are acceptable in general, meaning that he observes the religious obligations, especially the prayer, and avoids major sins, then there is no harm in marrying her off to him, especially given that she is emotionally attached to him and that there is no religious impediment to their marriage. Ibn ʻAbbaas, may Allah be pleased with him, narrated that the Prophet, sallallahu ʻalayhi wa sallam, said, “There is nothing like marriage for two people in love.” [Ibn Maajah]
It is permissible for you to be your sister's Wali (legal guardian) in this marriage contract if your father delegates you to do so, or to be a witness to the marriage. For more information, please refer to fatwa 83629 about the conditions for the validity of the marriage contract in Islam.
We would like to remind the girl's father that he shall be held accountable before Allah regarding her; he has to do whatever preserves her religiosity and honor. Allah, the Exalted, says (what means): {O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones...} [Quran 66:6]
As-Saʻdi said in his Tafseer (Quran exegesis):
“It means: O parents, your children are trusts deposited with you, and Allah has enjoined you to take care of them. You must strive to preserve their religious and worldly interests; you should teach, discipline, and protect them from corruption and evils. You should command them to obey Allah and adhere to Taqwa (piety and mindfulness of Allah). Allah, the Exalted, says (what means): {O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones.} [Quran 66:6] Children are entrusted to the parents; the parents either honor the trust or they neglect it and accordingly incur the relevant warning and punishment upon themselves.”
Allah knows best.