Who conquered the lands of Persia, and during whose reign was that?

The land of Persia was conquered in stages during the time of Caliph Umar ibn al-Khattab, the most significant of which was the Battle of al-Qadisiyyah in the 14th year of the Hijra, led by Sa'd ibn Abi Waqqas. The conquest was completed with the Battle of Nahavand in the 20th year of the Hijra, led by Nu'man ibn Muqarrin.