How can she be invited to Islam and her questions answered appropriately?

Islam is a religion of natural inclination (fitra), persuasion, and self-respect. Both white and black, educated and unlettered, and others may embrace it. Your concern with inviting the professor to Islam is good. Her lack of conviction may be due to reasons such as: poor presentation, weak material provided to her about Islam, the absence of good role models among Muslims, or her being among those who argue falsely. الدعوة (inviting people to Islam) is obligatory upon every Muslim, and it is a collective obligation (fard kifaya). Da'is (those who invite to Islam) should use wisdom and good exhortation, avoid harshness and severity, and exert their utmost effort in inviting people to Islam, as it carries a great reward.