All perfect praise be to Allah, The Lord of the Worlds and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Prayer is the basis of religion and one of the five pillars of Islam.Therefore, it should be performed in the right manner as well at the proper time since Allah, The most Exalted, said (What means):" For such prayers are enjoined on believers at stated times. [An-Nisa'/103]. In addition, if a person missed an obligatory prayer then it is a debt on him until he makes it up since the Prophet(PBUH) said (What means):"So pay Allah's Rights, as He is more entitled to receive His rights." [Agreed upon] Besides, he(PBUH) said (What means): He who forgets the prayer should say it when he remembers it, there is no expiation for it, except this." [Agreed upon].
Furthermore, making up missed prayers is valid at any time and doing so in their proper sequence is recommended as well. Yet, a person should observe the sequence of missed prayers in order to avoid scholars' different opinions in this regard. Further, they have differentiated between two cases concerning making up missed prayers: First: Whosoever missed an obligatory prayer with an excuse is recommended to hasten in making it up in order to be free from the liability as stated in [Boshra Al-Kareem Sharih Al-Muqadima Al-Hathramia]:" It is recommended to hasten making up prayers missed with an excuse, sleeping or forgetfulness and the like, so as to be considered free from the liability." Second: Whosoever missed an obligatory prayer without an excuse is obliged to make it up immediately even if it took all of his time save the times in which a person has a basic needs and other day-to-day obligatory prayers." The person who missed prayers without an excuse must perform them immediately, as a punishment." [Boshra Al-Kareem]."
Therefore, it is permissible to make up missed prayers as much as possible even if a person had to dedicate all his time to pray every missed prayer along day-to-day obligatory prayers. He should also perform prayers at their proper time and sequence since the Prophet (PBUH) was asked which deeds are loved most by Allah?" He replied, 'To offer prayers at their early (very first) stated times. " [Agreed upon]. And Allah knows best.