Answer
Wa `alaykum As-Salamu waRahmatullahi 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:
There is nothing wrong with making duaa for non-Mahrams.
Answering your question, Sheikh Ahmad Kutty, a Senior Lecturer and an Islamic Scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Allah describes the believers in the Qur’an: “And those who came after them say: “Our Lord! Forgive us, and our brethren who came before us into the Faith, and leave not, in our hearts, rancour (or sense of injury) against those who have believed. Our Lord! Your are indeed Full of Kindness, Most Merciful.“ (Al-Hahsr 59:10)
The Prophet (peace be upon him) further taught us to pray for one another. There is no reason to exclude women from this general imperative. We are not allowed to make an exception without clear evidence warranting it.
Therefore, women are encouraged to pray for other believers even as men are encouraged to do so. We have also precedents for this in the practice of the mothers of faithful such as `A’ishah and others (Allah be pleased with them all).
Allah Almighty knows best.