Is the prayer valid if the imam recited Al-Fatihah immediately after the first rak'ah inadvertently and performed the prostrations of forgetfulness (sujud as-sahw)?

The majority of scholars hold that the takbeerat of transition are Sunnah, while the well-known position among the Hanbalis is that they are obligatory. Therefore, whoever omits them out of forgetfulness should perform the prostration of forgetfulness (sujood as-sahw), and whoever omits them intentionally has invalidated their prayer. If the Imam omitted the takbeer for standing up for the second rak'ah out of forgetfulness and then performed the prostration of forgetfulness, then his prayer is valid, and the prayer of those behind him is also valid.