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.
First of all, we say that there is no harm on that woman in showing her interest in marrying that young man if he repents to Allah and observes the prayer regularly. Anas, may Allah be pleased with him, narrated, "Abu Talhah proposed to marry Umm Sulaym, may Allah be pleased with them, so she said to him, 'O, I swear by Allah, a person like you should not be refused, but you are a disbeliever, and I am a Muslim. So it is not permissible for me to marry you. If you embrace Islam, then I will consider that my dowry is your becoming Muslim and will not ask you for anything else.' He then embraced Islam, and his becoming Muslim was her dowry.'" [An-Nasaa’i – and he wrote a Chapter on this entitled: "The Chapter of embracing Islam as a dowry for marriage"]
However, she should not accept to marry him simply because he claims that he has repented and that he preserves the prayer; rather, it is more appropriate for her to wait and see until it becomes evident to her that he is truthful in his claim and that he is upright and is religious and has a good moral conduct, because we are guided by the Shariah to choose a person with such qualities.
The Prophet said, "If a man whose religion and moral conduct are pleasing to you proposes to you, let him marry; otherwise, there will be great mischief and corruption on earth." [At-Tirmithi and Ibn Maajah]
It was also reported that a man asked Al-Hasan Al-Basri, "To whom shall I marry my daughter?" He replied, "To the one who fears Allah, because if he loves her, he will honor her, and if he hates her, he will not be unjust to her."
If it is not predestined for them to marry and his heart remained attached to her, then he is not held accountable for his feelings over which he has no control, let alone her being accountable for it, as it is something beyond his control. If we presume that this attachment results in what is not pleasing to Allah, then it is he who will be held accountable and not her, and she is not considered the reason for it such that she would be accountable for it. He is obliged to strive against himself and fear Allah and avoid what displeases Him.
Allah knows best.