I say, and with God's success: If a disbeliever performs tayammum for his Islam, it is not permissible for him to pray with this tayammum; because one of the conditions for the validity of the intention is Islam, and he intended while being a disbeliever, so the tayammum of a disbeliever is not valid whether he intended a specific act of worship that is only valid with purification or not. He must perform tayammum again for prayer, unlike if he performed ablution without intention and then converted to Islam, his prayer is valid with this ablution. Likewise, if he performed ablution with intention and then converted to Islam; because the intention of a disbeliever is void due to lack of eligibility, and intention is not a condition for ablution. Refer to: Sharh al-Wiqayah p. 108, Al-‘Inayah 1: 115, and Rad al-Muhtar 1: 165, and God knows best.