How can a Muslim man residing in Germany help a European girl he wishes to marry after she embraces Islam, especially given her family problems that lead her father to expel her from the home, and is he permitted to assist her financially?

There is no objection to informing a non-Muslim girl of the desire to marry her, in order to encourage her to embrace Islam, and it is permissible to assist her financially for that purpose. However, extreme caution must be exercised to avoid any unlawful intentions. It is preferable to connect her with an Islamic center to undertake her دعوتها (invitation to Islam) and guidance, thereby avoiding temptation (fitna). If she embraces Islam and becomes righteous, then praise be to Allah. Otherwise, seek a righteous Muslim wife and avoid any contact that could lead to an unlawful relationship.