She claimed that she was pregnant with a child from him and had an abortion, and he paid the expenses

A woman who has a bad reputation and behaves badly claimed that she was pregnant from a friend of mine that she was pregnant. He is married with a young daughter and he swears that he has never had intercourse with her, although something happened between them, but it did not reach the level of intercourse. But she insisted that he was the father of the child in her womb. The solution was that she went to a doctor to abort the child, and because he was afraid of exposure and embarrassment that this woman could cause – because he is married and has a daughter, as I said – he paid for the abortion expenses. It turned out that she was pregnant with a child whose age was six days shy of three months. He deeply regrets what he did, and paying for the expenses of aborting a child whose conception he had nothing to do with. 
My question is: 
What is the Islamic ruling on this action? How can he repent from this deed? Is he regarded as a partner in the killing? How can he repent sincerely to Allaah from what happened? What should he have done, according to sharee’ah, when this girl claimed that he was the father of the child in her womb? I would like an answer soon. May Allaah reward you with good.

Praise be to Allaah.

Firstly: 

Allaah says (interpretation of the meaning): 

“And whosoever fears Allaah and keeps his duty to Him, He will make a way for him to get out (from every difficulty)”

[al-Talaaq 65:2] 

Your friend did not fear Allaah, so He did not grant him a way out. You say that he was intimate with that woman, but he did not have intercourse with her. This is taking lightly and being heedless about doing a haraam action with that woman, which is what led him to commit the second crime (abortion) and made him unable to ward off accusations against him and stand up to this woman properly, because he knew in his heart that he was not chaste and did not resist doing haraam things, even though Allaah has blessed him with a wife and a legitimate marriage. How can a wise man refrain from good, halaal pleasure and replace it with haraam and enjoy it? 

If your friend had kept himself chaste, Allaah would have granted him a way out, but he transgressed the sacred limits of Allaah and was punished by being caused to fall into another sin. As one of the salaf said:  One of the punishments of sin is further sin, just as the reward for good deeds is more good deeds. 

Secondly: 

So long as there is still some goodness in your friend, which is indicated by his regret for what has happened and his desire to repent, then he should note that repentance is not valid and accepted unless it meets three conditions: 

1 – Regret for what he has done. 

2 – Giving up the sin. So he must cut off all ties with this evil woman. It is strange that you say that your friend has a daughter. Would he like that for his daughter? No one would want this for their daughters. 

So he cannot repent if he is still in touch with this woman or any other. 

3 – He should resolve firmly never to go back to this sin again, and he should resolve to refrain from haraam things and protect himself and his family. He should beware lest he be tested with regard to the closest of people to him as a punishment for what he has done. 

He should strive hard in acts of worship, and pray regularly on time with the congregation in the mosque if he was careless about that before. He should read Qur’aan a great deal and attend classes, and give a lot of money in charity. 

Allaah says (interpretation of the meaning): 

“And verily, I am indeed forgiving to him who repents, believes (in My Oneness, and associates none in worship with Me) and does righteous good deeds, and then remains constant in doing them (till his death)”

[Ta-Ha 20:82] 

Let him make this sin the beginning of something good for him, by turning to Allaah and keeping away from sin. Many people may be better after sinning and repenting than they were before, if they repent properly and strive to better themselves. 

And Allaah is the Source of strength.