Purity: Performing Qaḍāʾ Prayers with Tayammum
Practical Laws of Islam as per the teachings of Ayatullah Sistani
Ruling 705:
If someone who cannot perform wuḍūʾ or ghusl loses hope in his legitimate excuse expiring, he can perform his qaḍāʾ prayers with tayammum. However, if afterwards his legitimate excuse expires, the obligatory precaution is that he must perform his qaḍāʾ prayers again with wuḍūʾ or ghusl. If he does not lose hope in his legitimate excuse expiring, then based on obligatory precaution, he cannot perform tayammum for qaḍāʾ prayers.
-Ayatullah Sistani, Practical Laws of Islam, Purification (Taharah)