Is it permissible for a person who has done tayammum to lead the prayer because there is no one else apart from him who can lead the prayer?.
It is permissible for a person who has done tayammum to lead in prayer people who have done wudoo' if he did tayammum for a legitimate shar’i reason to purify himself from minor or major impurity. It is permissible for him to lead in prayer those who have purified themselves with water, and there is nothing wrong with that. Even if there is someone else who is qualified to lead the prayer, but he (the one who did tayammum) leads them in prayer, there is nothing wrong with that if he is himself qualified to lead the prayer. End quote.
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah have mercy on him).