Is it permissible to marry a Filipino Catholic Christian woman residing in the UAE, knowing that she works and will stipulate the continuation of her work, and how can she be invited to Islam after marriage, and what is the ruling on returning her greeting of "Assalamu Alaikum"?

It is permissible for a Muslim man to marry a chaste Christian woman, based on the Almighty's saying: (and the chaste from among the believing women and the chaste from among those who were given the Scripture before you) Al-Ma'idah/5. The husband must invite her to Islam, and respond to her greetings with "wa alaikum assalam" if she greets clearly. The relationship between a man and an unmarriageable woman should either be with the intention of marriage or severed, to avoid temptation and forbidden شرعية matters.