What is the ruling on a girl attempting to invite a non-Muslim to Islam via chat, while showing others the conversations to avoid being in seclusion, and given that this matter is a dream she wishes to fulfill?

We ask Allah to reward you for your sincere intention and to grant you success in faith, righteous deeds, inviting to good, enjoining what is right, and forbidding what is wrong. This is the characteristic of believing men and believing women, as Allah Almighty said: "And the believing men and believing women are allies of one another. They enjoin what is right and forbid what is wrong and establish prayer and give zakah and obey Allah and His Messenger. Those - Allah will have mercy upon them. Indeed, Allah is Exalted in Might and Wise." There is no objection for a woman to invite a man to the truth if she observes the Sharia guidelines and avoids fitnah (temptation/strife). However, if a man can undertake the invitation, it is better to avoid fitnah. For safety is paramount. If you have a man invite him to Islam, you will have fulfilled the Hadith: "The one who points to good is like the one who does it."