How can a Hindu girl be encouraged to embrace Islam, so that her motive is faith in God and not marriage, taking into account her parents' rejection of Islam and her desire not to lie to them, all out of a wish to marry her and guide her to Islam?

A Muslim is not permitted to marry a non-Muslim woman unless she is a woman of the Book (Kitabiyah); otherwise, the marriage is null and unlawful. The primary goal of inviting a non-Muslim woman to Islam should be her guidance, as there is immense reward in that. It is forbidden for a Muslim to engage in an illicit relationship with a woman who is not lawful for him, as this is a reprehensible act that must be avoided. No one has the right to choose their religion; rather, one must embrace Islam, and whoever seeks a religion other than Islam, it will not be accepted from him.