The imam does not memorize the surahs, but rather memorizes portions of them which he recites in the prayer
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Fatwa number ( 18691 )
Q: We have an imam in our neighborhood who is not one of the memorizers of the Book of Allah. He memorizes some portions of the surahs, and he constantly repeats these portions in every prayer, meaning he has never recited anything other than these portions. Is this permissible?
A: The guidance of the Prophet (peace and blessings be upon him) regarding recitation in the loud prayers is that he would lengthen the recitation after the opening chapter in the Fajr prayer, reciting from the long surahs of the final part of the Qur'an, and he would recite from the middle surahs of the final part in the 'Isha' prayer, and he would usually recite from the short surahs of the final part in the Maghrib prayer, though he might recite otherwise in it. There is no harm in the imam reciting from portions of the surahs that he has memorized, because the recitation after the opening chapter is a recommended practice, but the imam should take care to memorize what is easy of the Book of Allah so that he can recite from it in the loud prayers, in accordance with the pure Sunnah.
And success is from Allah, and may Allah send prayers and blessings upon our Prophet Muhammad, his family, and his Companions.
Q: We have an imam in our neighborhood who is not one of the memorizers of the Book of Allah. He memorizes some portions of the surahs, and he constantly repeats these portions in every prayer, meaning he has never recited anything other than these portions. Is this permissible?
A: The guidance of the Prophet (peace and blessings be upon him) regarding recitation in the loud prayers is that he would lengthen the recitation after the opening chapter in the Fajr prayer, reciting from the long surahs of the final part of the Qur'an, and he would recite from the middle surahs of the final part in the 'Isha' prayer, and he would usually recite from the short surahs of the final part in the Maghrib prayer, though he might recite otherwise in it. There is no harm in the imam reciting from portions of the surahs that he has memorized, because the recitation after the opening chapter is a recommended practice, but the imam should take care to memorize what is easy of the Book of Allah so that he can recite from it in the loud prayers, in accordance with the pure Sunnah.
And success is from Allah, and may Allah send prayers and blessings upon our Prophet Muhammad, his family, and his Companions.
Source
www.alifta.gov.sa
The Arabic text is copied verbatim from the original source, without any edits.