The following is a draft translation from arabic.
Question: A woman was an atheist (unbeliever) then she adopted Islam, a Muslim wanted to marry her, so is her atheist father allowed to be her guardian in the marriage contract? If not, who then will be her guardian (Wali)?
The Answer: An atheist has no guardianship on the Muslim woman, if a woman adopts Islam then her father has no guardianship to get her married. As for your question about how would the atheist woman -who adopts Islam- get married, and who will be her guardian, the answer is as follows:
If she has a relative from her blood relationship (her brother, uncle….) and he already adopted Islam like her, then he will be her guardian, if she has more than one relative -from her blood relationship- who adopted Islam, the nearest in relationship to her will be her guardian in marriage, her Muslim brother is more entitled than her Muslim uncle….
If she has no blood relationship who adopted Islam like her, and she is not living in a country which rules by Islam -as is the case in the question- then the Muslim Shar’i judge if present in the country, on condition that he will be trusted to encourage her in her adoption of Islam and does not hinder her Islam or help her atheist family against her, but if he is not trusted, then the man who made her adopt Islam could be her guardian in marriage, or she could choose a Muslim man who acts justly, whom she is content to be pious, then he could be her guardian in marriage, he can finish the marriage contract for her according to Shari’ah, then the husband can notarize the contract to maintain the rights.
For knowledge -if the country of the woman rules by Islam, then the Sultan is her guardian, if she has no blood relationship, because Rasulallah (saw) says:
«لا نكاح إلا بولي والسلطان ولي من لا ولي له»
“There is no marriage without a guardian (Wali), and the Sultan is the guardian of he who has no guardian” reported by Ahmad from Ibn Abbas and Aisha –may Allah be content with them- the sultan is more entitled than the judge and who comes after him from those mentioned before.
By Sheikh Ata ibn Khaleel Abu al-Rashta