Who bears the penalty (Fidya) if one Muhrim shaves the head of another Muhrim with his permission?

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The Fidya is incumbent upon the one whose head was shaved, even if the shaver was a Muhrim and did so with permission. This ruling applies because Allah the Almighty stated, "And do not shave your heads until the offering reaches its destination" (Quran 2:196). Since it is understood that someone else might perform the action, the prohibition and thus the penalty are attributed to the person whose action was restrained, meaning the person whose head was shaved bears the consequence.