Answer
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:
Yes, it is permissible for a menstruating woman to kiss her deceased brother. Menstruating women are not allowed to fast and pray. Other than these two things, there is no difference between a woman in her menses and another who is not in her menses in terms of reading the Quran or being in the mosque or any of the other social or religious rituals.
Answering your question, Dr. Jasser Auda, Professor and Al-Shatibi Chair of Maqasid Studies at the International Peace College South Africa, states:
There are no restrictions on menstruating women except for two things; first, she is not allowed to fast but she has to make up the missed days later; second, she is not allowed to pray and she does not have to make up the missed prayers.
Other than these two things, there is no difference between a woman in her menses and another who is not in her menses in terms of reading the Quran or being in the mosque or any of the other social or religious rituals.
As for kissing a dead person, there is nothing wrong with that. Aishah (may Allah be pleased with her) reported that Abu Bakr kissed the Prophet (peace be upon him) after he had died. (Al-Bukhari)
Aishah also reported that the Prophet kissed the forehead of Uthman bin Mazhun after his death. At that time tears were flowing from the Prophet’s eyes. (Abu Dawud)
Therefore, a menstruating woman can kiss her dead brother.
Almighty Allah knows best.