All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Allaah made the right of divorce exclusive to the husband, so your friend has the right to divorce his wife in return for some compensation or without any compensation, or he can continue his martial life with her if he likes.
However, we advise him to follow the steps established in Islam to remedy his disobedient wife. The details are mentioned in the Fatwa: 85402.
If she does not change and continues her ill-behaviour then her husband may honor her desire for divorce. If he wants he may take something in return for divorcing her.
However, they may not be separated by living apart, as if they are neither married nor divorced. This is not allowed in Islam since it is contrary to the ruling of Allaah (interpretation of meaning): {….Then [after that], either keep [her] in an acceptable manner or release [her] with good treatment….}[2:229].
Allaah knows best.