What is the ruling on the prayer of a man who did not rise from the first prostration until the Imam stood for the next rak'ah, because he did not hear the Imam's takbir, and should he repeat it as Dhuhr or Jumu'ah if it is invalid?

If the worshiper misses prostrating with the Imam until the Imam stands for the second rak'ah, then the worshiper should perform the prostration and follow the Imam, and their prayer will be valid. However, if they abandon the prostration out of forgetfulness or ignorance and join the Imam, then that rak'ah is void, and they must perform a replacement rak'ah after the Imam's taslim, and their prayer will be valid. But if they do not perform the prostration nor a replacement rak'ah, then their prayer is invalidated, and they must make it up. If the prayer was Jumu'ah (Friday prayer), they should make it up as Dhuhr prayer, four rak'ahs.