If someone had intercourse with her husband during the night, and then woke up in the morning and found that she is menstruating, can she do Ghusl to cleanse herself from the Janaba?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

The menstruating woman is not required to perform Ghusl for Janaabah (state of sexual defilement). But if she performs Ghusl for Janaabah during her menstruation period, this Ghusl is valid for Janaabah and she becomes then pure from Janaabah.

As for the menstruation, its ruling continues until blood stops completely. So, the Ghusl from Janaabah does not influence the ruling concerning menstruation.

Allah knows best.