He committed zina with her and she got pregnant; can he marry her while she is pregnant or should she abort he foetus?
It is permissible for the one who committed zina to marry the woman with whom he committed zina if they are no longer regarded as zaani, which is after repenting sincerely. If she is pregnant, it is not permissible to do the marriage contract with her until her pregnancy ends, and the child is not to be named after the zaani according to the majority of scholars. Some scholars are of the view that the illegitimate child is to be called after the zaani if he acknowledges him. See the answer to question no. 33591
In Fataawa al-Lajnah al-Daa’imah it says: What is required of both of them is to repent to Allah then to give up this crime and regret what has happened in the past of committing immoral actions, and they should resolve never to go back to it and they should do a lot of righteous deeds in the hope that Allah will accept their repentance and turn their bad deeds into good deeds. Allah, may He be exalted, says (interpretation of the meaning):
“And those who invoke not any other ilaah (god) along with Allaah, nor kill such person as Allaah has forbidden, except for just cause, nor commit illegal sexual intercourse __ and whoever does this shall receive the punishment.
69. The torment will be doubled to him on the Day of Resurrection, and he will abide therein in disgrace;
70. Except those who repent and believe (in Islamic Monotheism), and do righteous deeds; for those, Allaah will change their sins into good deeds, and Allaah is Oft‑Forgiving, Most Merciful
71. And whosoever repents and does righteous good deeds; then verily, he repents towards Allaah with true repentance”
If you want to marry her, you have to wait until it is established that she is not pregnant by waiting for one menstrual cycle before doing the marriage contract with her. If it turns out that she is pregnant, it is not permissible for you to do the marriage contract with her until after the pregnancy ends, in accordance with the words of the Prophet (blessings and peace of Allah be upon him) that a man should not irrigate the crop of another with his water.
End quote from Fataawa al-Lajnah al-Daa’imah, Majallat al-Buhooth al-Islamiyyah, vol. 9, p. 72
It is not permissible to abort the foetus in order to get rid of the shame of zina. See the answer to question no. 13331.
And Allah knows best.