Prayer: Is the prayer valid if someone mistakenly recites al-Fātiḥah and another surah in the third rak‘ah?

Practical Laws of Islam as per the teachings of Imam Khamenei

Prayer: Is the prayer valid if someone mistakenly recites al-Fātiḥah and another surah in the third rak‘ah?

English:

Question #468:

If someone inadvertently reads the Fātiḥah and another chapter in the third rak‘ah of noon prayer, for example, and notices his mistake after finishing the prayer; will it be obligatory for him to repeat that prayer? And if he does not even notice his mistake, will his prayer be correct?

Answer #468:

In the given case, the prayer is correct.

-Imam Khamenei, Practical Laws of Islam, Importance and Conditions of Prayer