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.
Calling to Allaah The Almighty is obligatory on every Muslim as long as he is able to assume this task. However, Islamic regulations and limits should be observed at all times, because it is impermissible to enjoin what is good while violating the commandments of Sharee'ah. For example, it is prohibited for the one propagating Islam to address women (if a woman can do the task), mix with them, look at them, or meet them in seclusion.
Generally, most of those who call women to embrace Islam or to adhere to it commit some prohibited acts, such as engaging in conversation beyond the scope of Da‘wah, and this leads to suspicion and corruption. It is rare that a person manages to avoid doing this.
Therefore, we advise your friend not to assume this task himself, because it is always better to stay on the safe side. He could, however, try to assign this task to one of his Mahram women like his sister, mother or aunt. If this is not possible, he should refer the girl to any Islamic center. Otherwise, he could make use of books and audio material to call her to Islam.
If it is inevitable that he must speak to her, he should take a third party with him to protect them both from temptation. However, if he feels that both he and this girl could become subjected to temptation, then he must abandon this task, since it is better to protect him and others from harm.
Finally, it is important to note that it is prohibited in Islam to establish any relation with the opposite sex outside the bond of marriage. He must ask himself before establishing any relation; do I accept my sister or any of female Mahram to have the same relationship with a man?
Allaah Knows best.