Is it true that Allah gave Pharaoh a reprieve of 40 years before answering the supplication of Musa (peace be upon him) against him, because Pharaoh was dutiful to his mother, and that Allah punished him after his mother's death?

It has not been established that Pharaoh was dutiful to his mother, and the delay in his punishment was not due to that. Rather, exegetes mentioned that his punishment was delayed for forty years after the supplication of Moses and Aaron, peace be upon them. The delay might have been a way for Allah Almighty to lure him into complacency (istidraj), or for other reasons known to Allah.