Is the prayer valid if the imam performed one rak'ah and prostrated once, then said the taslim, and then one of the congregants stepped forward and completed the prayer, then performed the two prostrations of forgetfulness after the taslim?

It is not permissible for someone who has entered a fard (obligatory) prayer to break it unless there is a legitimate شرعي excuse. If such a situation occurs, for example, if one remembers that they are in a state of ritual impurity (حدث), they may appoint someone else to complete the prayer with the congregation. The congregants (مأمومون) may then either offer the salutation (تسليم) or wait for the appointed امام to complete his prayer. If the امام does not appoint a successor, the congregants may complete their prayers individually, or appoint a successor themselves before performing a verbal or physical pillar, or if the interval is not too long. If they appoint a latecomer (مسبوقًا) as successor, he must consider the prayer of the امام he replaced. If he does not consider his prayer, they should continue to follow him and offer the salutation with him after he completes his prayer. It is not permissible for those who lag behind the امام to speak; rather, they should use gestures. If the امام breaks his prayer and starts another, his prayer is valid, and he is not required to perform the prostration of forgetfulness (سجود سهو). If he performs it out of ignorance, his prayer is still valid. It is not permissible for the congregants to start a new prayer, but if they do, it is valid. If they continue to follow the امام with the intention of the first prayer and add to it, their prayer becomes invalid, unless they are ignorant of the impermissibility of this addition.