All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If this young man intends to marry this girl who has just converted to Islam in order to help her in being steadfast on Islam, teach her the religious rulings, and keep her away from those who want to drive her away from Islam, then this is something good.
If this girl has really embraced Islam, then her parents have no right in her guardianship. It is the Muslim community which should be responsible for looking after her if she has no Muslim guardian, as Allaah Says (what means): {…and never will Allaah give the disbelievers over the believers a way [to overcome them].} [Quran 4:141].
Therefore, the refusal of the parents of this girl to marry this young man has no religious effect. She can get married to him despite their refusal.
As regards the parents of this young man, he should convince them and inform them of his will to marry this girl, and clarify to them that he intended a praised religious objective [in marrying her].
If he explains to his parents with wisdom, it is most likely that they will approve of this marriage. However, if they do not approve of it, he is obliged to obey them as there is much good –whether sooner or later –in obeying them.
Allaah Knows best.