Does a divorce occur between a couple if the husband gives his wife the choice between living with him or divorce, and the wife refuses divorce, and then the husband sends her a message saying "The matter is over" after communication ceased? And does Islamic law compel the husband not to divorce if the wife refuses?

If a man gives his wife the choice between divorce and staying, and she chooses to stay, then divorce does not occur, according to the majority of scholars. As for the message "The matter is concluded," if the husband intended divorce by it, then it has occurred; otherwise, it has not. In all cases, if the husband explicitly pronounces divorce, or uses an allusive term with the intention of divorce, and he is aware of what he is saying, then divorce occurs, regardless of whether the wife accepts it or dislikes it.