Answer
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.
In this fatwa:
The mahr (dower) is the wife’s right. If she approves, there is nothing with investing mahr money.
Answering the questions about investing mahr money, Dr. Muzammil H. Siddiqi, Former President of the Islamic Society of North America, states,
If the woman did not specify the amount of money or the method of payment at the time of marriage, then they can make an agreement after marriage.
In case they do not agree, then whatever is the custom (urf) of the bride’s family is what will be followed.
If the dispute persists, then they should refer it to an Islamic judge.
Also, if the woman is requesting and she wanted her money to be invested, then there is no objection in investing mahr money.
Allah Almighty knows best.