When a person repents to his Lord, are the prayers which he missed prior to his repentance erased? Are they held against him? We asked Dr. Yusuf al-Qaradawi through the Internet, and he clearly stated that it is obligatory to make up the missed prayers. As this is not possible, what is the solution?

 

There is a consensus among the imams of the four schools of jurisprudence that one must make up missed prayers, because of the words of the Prophet (peace and blessings be upon him), which have been narrated by ‘Abdullah ibn ‘Abbas, may God be pleased with him, “Pay the debts you owe to God; a debt owed to God has more right to be fulfilled” (Bukhari).
Anas ibn Malik (may God be pleased with him) also narrated that the Prophet (peace and blessings be upon him) said, “Whoever forgets to perform a prayer is to pray it when he remembers: there is no other expiation for it” (Bukhari and Muslim).
Since it is obligatory for the one who has missed a prayer out of forgetfulness to make it up—though the sin and harm of missing the prayer are removed—then, there is an even stronger reason to apply it to the one who deliberately misses a prayer—thus hinting at the status of the greater by mentioning the status of the lesser.
Imam al-Nawawi (may God have mercy on him) said in his commentary of Sahih Muslim, "Some of the Zahirites (Literalists) maintained a deviant opinion [concerning this matter], saying that one does not have to make up a prayer which he has missed without an excuse. They claimed that missing a prayer without an excuse is so great that one cannot remove himself from its sin by making it up. This is an error and ignorance on the part of the one who said it and God the Almighty knows best."
Whoever has missed a prayer, whether a long or short time ago, must repent to God the Almighty and start making up his missed prayers. With each current prayer he must make up an old prayer of its like, and he can do just this instead of praying the sunna prayers associated with the obligatory prayers. This is because the reward of an obligatory act is greater than the reward of one that is supererogatory. The Prophet (peace and blessings be upon him) pointed out the superiority of making up a missed prayer with its like in a hadith narrated by Abu Qutada al-Ansari, may God be pleased with him, “Whoever prays the dawn prayer at its prescribed time is to make up with it its like” (Abu Dawud). Al-Khattabi said, “It seems that the order here is to convey the merit of praying it at its time." One must continue to do this for a period equaling the period in which he neglected his prayers and until he deems that he has most likely made up the prayers he has missed. Should he pass away before making them up, God will forgive him out of His grace and generosity if He so wishes.

God the Almighty knows best.
http://www.dar-alifta.org/Foreign/ViewFatwa.aspx?ID=617