As stated and ruled out by the major grand scholars such as Syed Khamanei that anything added in Salah even if it is a true statement is considered as an innovation and makes the prayer invalid. Regarding the third testimony in salah, why is that the third testimony is not recited by us Shia Muslims at the end of Salah in Tashahud when giving salams to the Prophet (PBUH) and what evidence indicates that it has been forbidden or that it was not done by the final Prophet (PBUH) or any of the 12 Imams?

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The evidence is that there is no evidence indicating that the Holy prophet did it.

The general advise in this regard is for one to follow the ruling of his or her Marja