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.
We advise you to link this sister with other pious sisters who have enough religious knowledge to repel her misconceptions about Islam. A woman calling another woman to Islam is more appropriate than a man doing so as this may lead to corruption [fornication or adultery].
If the girl whom you mentioned lives in another country than yours, then you may send her the addresses of some Islamic centres in her country if you have her e-mail address. You may also send her some books which talk about the bounties of Islam and that it is the true religion revealed by Allaah.
For more benefit about a man teaching a woman, please refer to Fatwa 85337, and to Fataawa 81671 and 82217 about establishing a friendship relation between a man and a woman.