Her period started after the time for prayer began – what is the ruling?

Praise be to Allah.

If the period starts after the time for prayer begins, e.g. it starts half an hour after the time for Zuhr prayer begins, then after she becomes pure (i.e., after her period ends) she should make up the prayer whose time began when she was still pure, because Allah says: 

“Verily, As‑Salah (the prayer) is enjoined on the believers at fixed hours” [al-Nisa’ 4:103]

But she should not make up the prayers from the time of her period because the Prophet (peace and blessings of Allah be upon him) said, in a lengthy hadeeth: “Is it not the case that when she is menstruating she does not pray or fast?” (Narrated by al-Bukhaari, 304; Muslim, 80). 

The scholars are agreed that a woman does not have to make up the prayers that she missed during her period. 

But if she becomes taahir (pure – i.e., her period ends) and there is still enough time left to do one or more rak'ahs, then she should pray the prayer during the time of which her period ended, because the Prophet (peace and blessings of Allah be upon him) said: “Whoever catches up with one rak’ah before the sun rises has caught up with Fajr prayer, and whoever catches up with one rak’ah before the sun sets has caught up with ‘Asr prayer.” (Narrated by al-Bukhaari, 579; Muslim, 607). So if she become pure at the time of ‘Asr and there is enough time left before sunset for her to pray one rak’ah, then she should pray ‘Asr. And Allah knows best.