Is it permissible for the Imam to recite verses from the beginning of a Surah in the first Rak'ah, then omit verses in the middle and recite the last verses of the same Surah in the second Rak'ah, such as reciting "Glorify the name of your Lord, the Most High...to...Indeed, He knows what is declared and what is hidden" in the first [Rak'ah], then "He has succeeded who purifies himself and remembers the name of his Lord" to the end of the Surah in the second, or is it better to maintain the sequence?

There is no harm for the Imam to recite part of a Surah in the first Raka'ah and then complete it in the second, due to the generality of Allah's saying: (So recite what is easy for you of the Qur'an). However, it is preferable to recite a complete Surah in each Raka'ah, or to start in the second Raka'ah from where he left off in the first. It has been reported that the Prophet, peace and blessings be upon him, used to recite a complete Surah, or recite the beginning of a Surah, and it is not preserved that he recited the ends or middles of Surahs.