Assalaamu alaikum. I recently read somewhere that Surah Al-Feel and Surah Quraish must be combined in the prayer, that they cannot be read separately as different surahs, and that this is the same for Surah Adh-Dhuha and SurahAsh-Sharh. Is this correct according to the Hanafi mathhab (school of thought)?

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger. 

This is incorrect both according to the Hanafi mathhab and the other mathhabs. A group of scholars argued that the soorahs of Al-Feel (no. 105) and Quraysh (no. 106) are one soorah, however, well-versed scholars refuted this view, including the Hanafi scholar Al-Aloosi. They explained that tawaatur (collectively contiguous narrations) are sufficient to prove that they are two separate soorahs.

Al-Aloosi said:

“A group of scholars argued that they (soorahs Al-Feel and Quraysh) are one soorah, and they relied on the fact that Ubayy ibn Kaʻb did not separate between them with the Basmalah (Bismillah Ar-Rahman Ar-Raheem) in his copy of the Quran ... The statement that they are two separate soorahs is supported by the fact that the rhetorical styles of the verses of the two soorahs are different. It is known that establishing that they are two separate soorahs through tawaatur eliminates the need for any further proof.”

As for Soorah Adh-Dhuha (no. 93) and Soorah Ash-Sharh (no. 94), Al-Aloosi, who is a Hanafi scholar, as we mentioned above, cited the view suggesting that they are one soorah on the authority of Taawoos and ʻUmar ibn ʻAbd Al-ʻAzeez, and he said that this is the view held by the Shiites and refuted it with the established tawaatur that they are two separate soorahs. Al-Aloosi said:

“It has been reported on the authority of Taawoos and ʻUmar ibn ʻAbd Al-ʻAzeez that they held that they (Adh-Dhuha and Ash-Sharh) are one soorah, and they used to recite them combined in one rakʻah (unit of prayer) without separating them with Basmalah. The Shiites also did this as cited by At-Tabrasi ... The truth is that the decisive factor in this regard is the riwaayah (chains of narration) not the diraayah (deduction). It has been narrated through tawaatur (collectively contiguous chains of narration) that they are two separate soorahs that should be recited independently and separated with the Basmalah...”

Hence, it becomes clear that the statement that you read is incorrect and that each of the four soorahs that you mentioned is an independent soorah that may be read alone without combining it with another soorah.

Allaah knows best.