What is the ruling on prosthetic limbs, and is it permissible to attach a prosthetic hand to a person upon whom the Hadd penalty for theft has been carried out?

Firstly: It is permissible to use prosthetic limbs when an original limb is lost. This is supported by the hadith of Arfajah ibn Asad (may Allah be pleased with him) when he fashioned a nose of gold, and by the resolution of the Islamic Fiqh Council affiliated with the Muslim World League.

Secondly: It is permissible to attach a prosthetic hand for someone who has had their hand amputated due to the حد السرقة (punishment for theft), and there is nothing to prevent this. Scholars have differed regarding the reattachment of the original hand amputated due to the حد السرقة. The majority of contemporary scholars prohibit it. Those who prohibit it argue that the amputation was legislated for deterrence and exemplary punishment, and reattaching the hand contradicts this. Furthermore, the Prophet (peace be upon him) commanded the cauterization (حسم) of the thief's hand and its display. However, a prosthetic hand does not take the place of the original hand, and attaching it does not contradict the cauterization, nor is there any authority over the thief regarding its attachment after the amputation.

In summary: There is no objection to a thief attaching a prosthetic hand after their hand has been amputated.