Is it permissible to delay prayer and make it up later because of a migraine?
Question

                Is it possible to delay prayer and make it up at another time because of migraine and headache?.
Praise be to Allah.
    Firstly: 

    Allah has commanded his slaves to establish prayer at the 
    times that He has prescribed for it. He says (interpretation of the 
    meaning):

    “Verily, the prayer is enjoined on the believers at fixed 
    hours”

    [an-Nisa’ 4:103]. 

    He has made the timings of the prayer flexible for His 
    slaves; He has appointed a beginning and end for them, and the time between 
    the beginning, which is the best of its time, and the end, is sufficient 
    time to pray. Whoever cannot pray at the beginning of the time has the 
    option to pray until the end of that time comes. In the hadeeth of Jibreel 
    (peace be upon him) it says that after the Prophet (blessings and peace of 
    Allah be upon him) had offered the five obligatory prayers at the beginning 
    of their times and the end, Jibreel said to him: “O Muhammad, these are the 
    times of the Prophets who came before you and the time (for each prayer) is 
    between these two times.”

    Narrated by Abu Dawood, 332; classed as saheeh by al-Albaani 
    (may Allah have mercy on him) in Saheeh wa Da‘eef Sunan Abi Dawood, 
    1/393 

    With regard to delaying the prayer until the time for it has 
    ended, that is not permissible except in the case of one who has an excuse, 
    such as if he fell asleep or forgot, because the Prophet (blessings and 
    peace of Allah be upon him) said: “There is no negligence in (the case of) 
    sleep; rather negligence is in the one who does not offer a prayer until the 
    time for the next prayer comes.”

    Narrated by Muslim, 1099 

    Secondly: 

    If a person is sick in that it is difficult for him to offer 
    a prayer at the specified time, whether at the beginning or at the end, and 
    he is also unable to offer the prayer standing or sitting or lying on his 
    side, according to the report which confirms the concession granted to one 
    who is sick, then he may put two prayers together, Zuhr and ‘Asr together, 
    and Maghrib and ‘Isha’ together, putting them together either at the time of 
    the earlier prayer or at the time of the later prayer, according to whatever 
    is easy for him. And he should offer Fajr prayer at the proper time, until 
    the reason that was preventing him from praying on time is no longer 
    present. 

    Ibn Qudaamah (may Allah have mercy on him) said:

    The kind of sickness that makes it permissible to put two 
    prayers together is that which makes it too difficult to offer each prayer 
    at its proper time because of hardship and weakness. Al-Athram said: it was 
    said to Abu ‘Abdullah: Can the sick person put two prayers together? He 
    said: I hope that he may do that if he feels too weak and is not able to do 
    anything other than that.

    End quote from al-Mughni, 2/59 

    And Allah knows best.