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

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 Allaah says: 

“Verily, As‑Salaah (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 Allaah 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 Allaah 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 Allaah knows best.