Is it obligatory to make up the Asr prayer after purification from menstruation if its time expired due to travel and the menstruation period began before making it up?

It was obligatory for you to pray the Asr prayer at its prescribed time, and you must now make it up with repentance and seeking forgiveness.

As for the Maghrib prayer, which you were menstruating during its time, scholars differ regarding the obligation of making it up: Hanafi school: If menstruation occurs during the prayer time, the prayer is dropped. Maliki school: If menstruation occurs during a shared prayer time, both prayers are dropped. If it occurs during a time specific to one of them, the specific one is dropped, and the other is made up. Shafi'i school: If a period of time passes that is not sufficient for the obligatory prayer, there is no make-up. If a period of time sufficient for the obligatory prayer passes, then making it up is obligatory. Hanbali school: If one is able to perform the opening takbir at the beginning of the time, and then menstruation occurs, making up the prayer becomes obligatory.

The most cautious approach and that which absolves one's responsibility is to make up the Maghrib prayer immediately after becoming pure and performing ghusl, because it was a prayer that became obligatory upon you at the beginning of its time, and you had sufficient time to perform it.