A man had sex with his wife who then reported she was feeling the pain of her menses starting. What does Islam say about this and how can he seek forgiveness of Allah?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Having sex with one's wife during her menses is forbidden. Allah Says (interpretation of meaning): {They ask you concerning menstruation. Say: that is an Adha (a harmful thing for a husband to have a sexual intercourse with his wife while she is having her menses), therefore keep away from women during menses and go not unto them till they have purified (from menses and have taken a bath). And when they have purified themselves, then go in unto them as Allâh has ordained for you (go in unto them in any manner as long as it is in their vagina). Truly, Allâh loves those who turn unto Him in repentance and loves those who purify themselves (by taking a bath and cleaning and washing thoroughly their private parts, bodies, for their prayers, etc.).} [2: 222].
Menses that is regarded in Shari'a is the flow of known menstrual blood. So, if your friend had sex before the blood began there is no harm even if she started feeling the pains of menses. However, it is better to avoid having sex in this case lest the menses starts during sex.
If he had sex with her after beginning the menses, he has to pay expiation according to some scholars. The expiation is giving one Dinar or half Dinar of gold in charity. A Dinar is equal to four and one forth grams. The evidence for this is the narration reported by Abu Dawood , al-Nasa'i from Ibn Abbas (Radiya Allahu Anhu) that the Prophet (Sallallahu Alaihi wa Sallam) said about a person: "Who had intercourse with his wife while she was menstruating. He must give one Dinar or half a Dinar in alms" .
Allah knows best.