What is the ruling on performing the prostration of forgetfulness (sujud al-sahw) due to correcting an error in the transitional takbir after recalling a fatwa stating that the prayer is not invalidated by this, and does this prostration invalidate the prayer?

If the melody in the transitional takbirat changes the meaning, then it is like omitting them. If it was due to forgetfulness or ignorance, it is compensated for by the prostration of forgetfulness (sujud al-sahw) according to the Hanbalis. However, according to the majority of scholars, the prayer is not invalidated by omitting them or by a melodic error in them. As for adding an extra takbir in the wrong place due to forgetfulness, scholars have differed on the permissibility of sujud al-sahw for it, with two opinions: some consider it permissible as a recommendation, not an obligation, because it rectifies something that is not obligatory; others do not consider it permissible.