Is the saying, "May Allah and His Messenger establish it," upon hearing the Iqamah for prayer correct? And is there any Hadith from the Messenger of Allah, peace and blessings be upon him, concerning it?

It is sunnah for the one who hears the iqamah to say, when the one calling the iqamah says "Qad Qamat As-Salat, Qad Qamat As-Salat" (The prayer has been established, the prayer has been established): "Aqamahallahu wa adamaha" (May Allah establish it and perpetuate it); because this has been reported from the Prophet, peace and blessings be upon him. The jurists from the Hanafi, Shafi'i, and Hanbali schools have adopted this. As for the addition of "wa Rasuluhu" (and His Messenger), it is not reported in the hadith.