Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother, we commend your eagerness to become well acquainted with the teachings of Islam, which is the way Allah has chosen for the welfare of His servants.
First of all, we would like to make it clear that Islam is the religion of morality, decency, and purity. Muslims are people of values and good ethics. Therefore, it is not an Islamic behavior to even look with desire at a woman other than his wife, let alone to be in love with another woman. Your friend should fear Allah and sincerely repent and seek Allah’s forgiveness.
In response to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Your friend must stay away from this woman who is already married. He is harboring an adulterous desire, which is clearly one of the gravest sins in Islam. He should cleanse his heart by repentance and occupying himself with good deeds. Remember, we cannot justify adultery by saying they had been in love in the past. Adultery is adultery, and its consequences are extremely serious in Islam.
Almighty Allah says: “And true servants of Allah are)those who cry not unto any other god along with Allah, nor take the life which Allah hath forbidden save in (course of) justice, nor commit adultery and whoso doeth this shall pay the penalty; the doom will be doubled for him on the Day of Resurrection, and he will abide therein disdained for ever; save him who repenteth and believeth and doth righteous work; as for such, Allah will change their evil deeds to good deeds. Allah is ever Forgiving, Merciful. And, whosoever repenteth and doeth good, he verily repenteth toward Allah with true repentance.” (Al-Furqan 25:68-71)
So, you should advise your brother to take the thought of her out of his heart totally and dedicate himself to repentance and good works so that Allah may forgive him.
I recommend you to give him the book entitled Purification of the Soul, published by Dar Al-Firdous, UK.
Allah Almighty knows best.