Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
After doing Tayammum, one becomes pure and may do any of the acts requiring prior purification such as praying and touching the Quran.
In his famous work, Fiqh As-Sunnah, Sheikh Sayyid Sabiq, elaborates on the subject as follows:
After doing Tayammum, one becomes pure and may do any of the acts requiring prior purification such as praying and touching the Quran. He does not have to perform Tayammum during the time of prayer, and he may pray as many prayers as he wishes (unless he nullifies it), exactly as he can after performing the regular ablution.
Abu Zharr reported that the Prophet (peace be upon him) said, “The soil is a purifier for a Muslim, even if he does not find water for twenty years. Then if he touches water, that is, to make ablution, and so on, it would be good.” (Ahmad and At-Tirmidhi who said it is an authentic Hadith.)
Almighty Allah knows best.