Praise be to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, his family and his companions.
Wa alaikum assalam wa rahmatullahi wa barakatuh.
As to what follows:
There is no difference of opinion among the scholars in that when a woman finishes her menses before the ending of a fixed time of a prayer she is obliged to perform that particular prayer. However they differed with regards to the time that is obligatory for her to perform the prayer.
The Hanbalite and Shafite scholars are of the opinion that if she can manage to do takbiratul Ihram (first Takbir) by the time of purification then qadha is compulsory on her.
The Malikite scholars are of the opinion that qadha is compulsory on her if she can manage to make one rak’ah at the time of purification.
The scholars went on to differ regarding the necessity of making qadha on a prayer that can be joined with another prayer, for instance, if she purifies herself during Asr time, is it obligatory for her to make qadha for Dhuhr swalah?
The scholars are of 2 opinions regarding this issue.
First opinion: It is obligatory for her to perform Dhuhr and Asr, this is what is held by the majority of scholars from the Tabi’een and those who came after them from the Jurists of the different schools of thought.
Second opinion: It is NOT obligatory for her to perform any swalah except that which falls within the time that she purifies herself in, this is the view held by al-Hasan, al-Thawri and Hanafites. It is also the stronger opinion with respect to proof.
It is not obligatory for her to pray just immediately after purifying herself, but what is safer is for her to pray the 2 swalahs if she becomes pure just before the end of a prayer time. This was said by a group of sahabah, among them were Abdul Rahman Ibn Awf and Ibn Abas (may Allah be pleased with them)
And Allah knows best.

Your brother,
Dr. Khalid al-Muslih
27 / 9 / 1427 AH