How should a person who is imprisoned and cannot find clean water or pure earth for tayammum perform their prayer?

According to the preferred opinion among the Hanafis, a person who is imprisoned and cannot find water for ablution or anything of the earth’s type suitable for tayammum should perform the prayer movements out of respect for the prayer time, and then make up the prayers after being released. (Kâsânî, Bedâ’i, 1/50; Ibn ‘Abidin, Radd al-Muhtar, 1/80) The valid view in the Shafi‘i school is also the same. (Nawawi, al-Majmū‘, 2/323) According to the Hanbalis, however, since prayer can be performed in this state, there is no need to make it up later. (Ibn Qudamah, al-Mughni, 1/184)

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu