Q: Is it permissible for the Imam to recite a portion of a chapter after reciting al-fatiha or does he have to read an entire chapter?
A: It’s recommended to read an entire surah after al-Fatihah in the first 2 rakahs. The Imam should select from Qaf to al-Mursalat for Fajr, al-Duha to al-Nas from Maghrib, and al-Naba to al-Layl for the remaining prayers. It is permitted to read any combination of surahs.
It is permissible to a read long verse or a portion of a chapter and is not disliked to read something short in Fajr due to some excuse such as illness, fear, or travel. It’s also permitted to read something longer in Maghrib.
Source: Sharh al-Muntaha