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, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
First of all, we would like to warn the questioner that friendship between men and women as it is known nowadays is impermissible in Islam, because it results in many indecencies that Islam came to prevent in essence and means. This does not mean that you discontinue all communication with this woman who desires to embrace Islam. However, any communication such as must be done within the boundaries of Islamic regulations. Specifically, you must not meet her in seclusion, nor may you look at her. Furthermore, your conversation with her should be restricted to necessary matters related to inviting her to Islam. Having said that, in principle inviting her must be done by one of the sisters as this is better and safe. If this cannot be achieved, then you may do it while adhering to the above limits.
For further encouragement, we would like to inform you of a Hadeeth in which the Prophet, sallallaahu ‘alayhi wa sallam, explained that being a cause through which Allaah The Exalted Guides a single person to Islam is more beneficial to a Muslim than receiving a huge fortune. [Al-Bukhari]
As for your question about what this woman should listen to or read, we refer you to the multimedia and article sections of our website.
Allaah Knows best.