Is the Christian colleague's saying to the Muslim woman, "Recite the Mu'awwidhat over your daughter" an indication of her belief in the Holy Qur'an and a harbinger of her potential conversion to Islam? And is inviting a disbeliever to guidance and offering her a gift considered an act of forbidden loyalty to Christians? And is it permissible to continue inviting her to Islam?

Your colleague's advice about ruqyah (definition) does not necessarily mean she believes in the Quran; rather, she may have seen its benefit. Your supplication for her guidance is permissible. There is no harm in giving her a gift to encourage her towards Islam. We advise you to use da'wah methods such as gifting her books and pamphlets that invite to Islam, and to increase your supplication for her. As for the reward simply for supplication, we hope you will have a share, even if the hadith (definition) refers to guiding someone to Islam and introducing it to them. Strive in inviting her and supplicating for her, so that your reward may be great and the objective achieved.