Should she agree to marry a man who lives in a kaafir country?

Praise be to Allah.

If the one who has proposed marriage is religiously committed and of good character, and his living in Sweden is permissible according to sharee’ah, or he wants to live in your country, then pray to Allaah for guidance (istikhaarah) and accept his proposal, because the Prophet (peace and blessings of Allaah be upon him) said: “If there comes to you one whose religious commitment and attitude pleases you, then marry [your female relative who is under your care] to him, for if you do not do that, there will be tribulation on earth and much corruption.” Narrated by al-Tirmidhi (1804) from Abu Hurayrah; classed as hasan by al-Albaani in Saheeh al-Tirmidhi.                    

If this young man is living there in order to call people to Allaah and he wants a wife who will help him in that, then this is the best of deeds. This is the mission of the Prophets (peace be upon them). Allaah says (interpretation of the meaning): 

“And who is better in speech than he who [says: ‘My Lord is Allaah (believes in His Oneness),’ and then stands firm (acts upon His Order), and] invites (men) to Allaah’s (Islamic Monotheism), and does righteous deeds, and says: ‘I am one of the Muslims’”

[Fussilat 41:33]

We ask Allaah to help you to do all that is good. 

For more information on the conditions of staying in the kaafir lands, see questions no. 14235 and 27211. 

And Allaah knows best.