What is the Sharia's advice to a friend who wishes to invite a non-Muslim girl to Islam?

Calling people to Allah is an obligation upon every able Muslim. The caller must adhere to the manners of Islam. It is not permissible to call to good by committing an evil, such as intermingling with women, being in seclusion with them, or looking at them. It is common for those who call women to fall into transgressions, so it is advisable to avoid calling women. One can delegate a mahram (definition) to do this, or direct the sister to Dawah centers for communities, or use books and tapes. If speaking is necessary, it should be in the presence of others to protect oneself from suspicion. If one fears fitna (temptation/strife), then one should keep away, for rectifying oneself is more important. It is not permissible to establish an unlawful relationship with a non-mahram woman.