I say, and with God's help: It is valid for him to perform tayammum after requesting water from someone who denied him: so if he prays after being denied and then is given water by the one who denied him, the tayammum is only invalidated now, and he does not need to repeat what he has already prayed. See: Ghinayat Al-Mustamli p. 69, Radd Al-Muhtar 1: 167, and God knows best.