Should he encourage a relationship between a Muslim man and a kaafir woman so as to protect her from evil and call her to good?!
Although we appreciate your keenness for that which is good and your intention to do what is best for this woman, we think that you are not doing the right thing by encouraging friendship between her and that Muslim man. How many of those who seek to do good fail to achieve it. The rulings of Islam should be our starting point in our actions and we should not be ruled by our emotions which go against the laws of Allaah.
You know that any haraam relationship between a man and a woman leads to many things that are contrary to Islam and may lead to falling into major sin, so how can such a relationship be a means of achieving good for the people involved?
Relationships between women and men outside the framework of shar’i marriage are haraam.
Moreover, your fear for this woman is making you expose your Muslim brother to temptation, so this woman will be a cause of your brother's temptation and may lead him to sins that doom a person to Hell and to immoral actions.
Now you are committing a haraam action in the hope of achieving some purpose which may or may not be achieved. Such things are not permissible according to sharee’ah.
You can achieve your goal in protecting this woman against evil and calling her to Islam through a woman -- like her -- who is Muslim and is close to her; thus you can call her to goodness and warn her against evil.
For ways in which a Muslim sister could call this woman to Islam, see the answer to question number 69876.
To sum up:
It is not permissible for you to encourage this haraam relationship; rather what you must do is advise them that this relationship is haraam according to Islam and that no one knows the unseen except Allaah. This may be a cause of her becoming Muslim because of what she sees of Islam’s respect for women and how it protects them.
We ask Allaah to guide you and her.
And Allaah knows best.