The answer given to the question by the office of Grand Ayatollah Khamenei is as follow:
The last time for performing Maghrib and Isha prayer is at canonical midnight. (i.e: 11 ¼ hours after, the canonical noon).
The precaution states that if one hasn’t performed one’s salat before the above deadline, one ought to perform it before dawn (fajr) with the intention to fulfill that which lies upon one’s shoulder i.e. that which you are responsible to perform it as (ma fi al-dhimma[1]) intention. Then after that, it will become Qaza[2]. In fact, His opinion on the matter of performing prayers after midnight or the canonical midnight is similar to Imam Khomeini’s decree.
In Tahrir ul-Wasilah, Imam Khomeini mentions that the time for performing maghrib and ‘isha salats starts at maghrib (when the redness over the eastern horizon disappears) and ends at midnight. The specifically allocated time for maghrib salat is on a par with the average time taken to perform three units (rak’aats) of salat from sunset onwards. Therefore, performing the ‘isha salat during this period is not permissible. The specific time for performing Isha prayer is on a par with the average time taken to perform four units for the one who is present at his/her homeland and two units for traveller, before midnight. Performing Maghrib prayer during this period is not permissible.
Therefore, the maghrib salat becomes qaza when the remaining time for performing isha salat is on a par with the average time taken to perform four units (for the present) and two units (for traveller). If someone postpones his/her maghrib and isha prayers at midnight (either intentionally and compulsory) and then wants to perform them from midnight till morning Adhan, according to the precaution he/she outs to perform them neither with Ada (on-time) intention nor with Qaza but as ma fi al-dhimma[3].
The answer given to the question by other Marja is as follow:
Office of Ayatollah Fazil Lankarani (may Allah grant him long life):
You will be able to perform your prayer until morning Adhan without the intention of Qaza and Ada. However, it would require the Qaza intention if it is performed after morning Adhan.

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