Is the prayer of one who did not hear the imam's voice as he rose from prostration, but caught up with him when he said the takbir for bowing, and then performed two prostrations of forgetfulness after finishing the prayer, invalidated?

If a congregant lags two pillars behind the Imam due to an excuse, and catches up before the Imam rises from bowing, then their rak'ah is valid and their prayer sufficient, and they are not required to repeat it. Prostration of forgetfulness (sujud (definition) as-sahw) in this case is considered an unintentional addition of the same type as the prayer and does not invalidate it. It is obligatory to learn the rulings of individual obligations (fard ayn) such as prayer and purification.