Can a guy Mary a girl whom he fornicate with?

They committed zina then they got married, and they are asking whether the marriage is valid

Question

Two people got married in accordance with sharee’ah and as enjoined by Allaah, but before marriage they used to get together and be intimate with one another like man and wife. What is the ruling on their marriage; is it valid or invalid? What is the expiation for what they used to do?.

Firstly:

Zina (fornication, adultery) is a serious crime and a major sin which takes away the quality of faith from a person, and exposes him to punishment and humiliation unless he repents. Allaah says (interpretation of the meaning):

“And come not near to unlawful sex. Verily, it is a Faahishah (i.e. anything that transgresses its limits: a great sin, and an evil way that leads one to hell unless Allaah Forgives him)”

[al-Isra’ 17:32]

and the Prophet (peace and blessings of Allaah be upon him) said: “No adulterer is a believer at the time when he is committing adultery” Narrated by al-Bukhaari (2475) and Muslim (57).

And he (peace and blessings of Allaah be upon him) said: “If a man commits zina, faith comes out of him and hovers over him like a cloud, then when he stops, faith returns to him.” Narrated by Abu Dawood (4960) and al-Tirmidhi (2625); classed as saheeh by al-Albaani in Saheeh Abi Dawood.

The Prophet (peace and blessings of Allaah be upon him) has told us of the punishment that those who commit zina will receive in their graves before the Hour begins, and that they will be punished with fire. Narrated by al-Bukhaari (1320).

Because of the abhorrent nature of this crime, Allaah has decreed that the punishment for it should be stoning to death if the person is married and flogging if he was not married.

Secondly:

 It is not permissible for a man or woman who has committed zina to get married until after he or she has repented, because Allaah says (interpretation of the meaning):

An-Nur 24:3

The fornicator does not marry except a [female] fornicator or polytheist, and none marries her except a fornicator or a polytheist, and that [i.e., marriage to such persons] has been made unlawful to the believers.

 If they had both repented to Allaah before getting married, and they regretted the haraam things that they had done, then their marriage is valid. But if they did the marriage contract before they repented, then the marriage is not valid and they have to repent to Allaah and regret what they have done, and resolve not to do such a thing again, then they should make a new marriage contract. 

And Allaah knows best.