I appreciate @Ahmadi's research and answer but, I wasn't 100% satisfied. I would like to extend the answer further.
I have got 2 different perspectives according to both perspectives the Mahr should be given to the bride even after divorce (even if it is demanded by wife).
It is best to give Mahr at the time of marriage. If you can not, then it becomes a due on you. So, even if you get divorced (no matter who initiated) the due amount should be given to the bride.
If you don't give Mahr at the time of marriage then you promise to give it later.
According to the first verse of Surah al-Ma'idah, Allah called upon the believers:
"O you who believe! Fulfill your promises." [5:1] : source
So, no matter if you you get divorced, you have to fulfill your promise.