All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Islam is the religion of truth and justice. So, nobody should have any doubt about this fact as this is the religion of Allah The Almighty, The All Knowing.
Indeed, the Rulings, Verdicts, and Orders of Allah are all for the wellbeing of humanity in all fields of life.
No doubt, preserving the matrimonial life in its best form has been given a great deal of importance in the Sharee’ah.
Allah has stipulated laws that preserve the family's well-being and continuation. Allah describes the marriage contract as a strong convenant. Allah Says (what means): {…and they have taken from you a solemn covenant?} [Quran 4:21]
It is like the convenants that Allah took from His Prophets.
Allah Says (what means): {And [mention, O Muhammad], when We took from the prophets their covenant and from you and from Noah and Abraham and Moses and Jesus, the son of Mary; and We took from them a solemn covenant.} [Quran 33:7]
In principle, the marriage contract is supposed to be forever; i.e. till death. The couple in that case will enjoy fully all the benefits of marriage, and the objective behind the marriage itself will be achieved. This is why Allah exhorted the husbands not to divorce their wives.
Ibn Al ‘Arabi said while interpreting this verse: “If the husband hates some behaviour of his wife and feels that he does not like her, he should try to find out the reasons for that. If the woman did not do any immorality (Zina and the like) and did not try to prevent him from sleeping with her, then he should be patient with her and endure what she does as that would be better for him.”
Abu Hurayrah narrated that the Prophet said: “A believing man should not hate a believing woman; if he dislikes one of her characteristics, he will be pleased with another.” [Muslim]
So the man is asked to bear his wife's mistakes. Now, if the wife is patient with her husband, likes him very much, does everything to please him and does not complain about any short comings from his side, then all the scholars are agreed that it is very dislikable for him to divorce her. Some scholars like Imam Ahmad even believe that it is forbidden for such a man to divorce his wife. Their evidence for this is that breaking such a relation is like spoiling wealth, which is forbidden.
The Prophet said: “There should be neither harm nor reciprocal harm.”
Imam Ibn Taymiyyah said: “Divorce is originally an act which Allah hates. It is even the most hated lawful act for Allah. In fact, Allah has made lawful only the divorce that people need desperately just like the lawfulness of unlawful things in dire necessity.”
So, we advise this man not to divorce his wife. We advise him to fear Allah in this woman who accepted him and who does not want to complain about his situation. In fact, she has given up her right just to stay with him. He should know that Islam urges him to stay with her and not divorce her as long as she is in the state described in the question.
On the other hand, the divorced woman should not fear to be rejected by other people. In fact, it is her behaviour which will determine how people look at her. If she is steadfast and pious and if her behaviour is good, people will deduce from her behaviour that she was not divorced for something bad. She was divorced only for some reason beyond her will. If she continues to be a good woman, Allah might provide her with a husband better than her former husband.
Allah knows best.