Yes his prayer is correct as raising hands is only a Sunnah act
Fatwa No: 86516

Question

Is Refedain (raising hands in prayer) is compulsory. If one doesn't raise hands in prayer, is that prayer is acceptable?

Answer

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  `alayhi  wa  sallam ( may  Allaah exalt his mention ) is His slave and Messenger.

Raising hands during the prayer is not one of the obligations of the prayer and the prayer does not become void by leaving it. However, raising hands is a Sunnah and the Prophet  sallallaahu  `alayhi  wa  sallam ( may  Allaah exalt his mention ) used to raise his hands at four positions in the prayer: when starting the prayer [Takbeeratul-Ihraam -the Takbeer for starting the prayer], while bowing down [Rukoo'], while raising from the bowing down position, and while raising from the first Tashahhud.

As for the question of the brother, is the prayer valid without raising hands?; then we inform you that the acceptance of the prayer depends on two factors: having pure intention and fulfilling all the obligations and conditions of the prayer.

However, observing the Sunnah and desirable acts besides the obligations is recommended since it increases the reward and makes the prayer more entitled to be accepted by Allaah.

Allaah Knows best.

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