Different transmissions for reciting various versions of a same mantra acc. to any of Vajrayana branches

Tashi delek! My question concerns the mantra reciting in Vajrayana tradition, where some Buddhist deities (not to be confused with the mundane ones) may have several versions of a same mantra. That is, a mantra of a same deity may be either longer or shorter according to different sutras and dharanis. In Vajrayana, it is also very important to receive a direct transmission of energy from guru (lama) before reciting any mantra. My question is, can a Vajrayana practitioner recite another version of the same mantra if she or he has already (in a given reincarnation) received from her or his guru a transmission for receiting another version of the same mantra? A reference to any root texts of any Vajrayana branch (Gelug, Sakya, Nyingma, Kagyu or Jonang) would be a great help.