I'm trying to figure out how it works for you. Let's say Black checkmate the white King while taking a white Pawn. Black says "checkmate", and White plays if, as you say, Black has to take a turn. So White plays while his King is checkmated. Either he plays another piece while leaving his King in check or he plays his King by placing it on a square where it is also in prise, as it was checkmated. Then, and only then, Black seizes the White King (so a black piece is now on the King's square) and White's Prince is becoming a King. Correct?
In such a case, it is strange that White plays while his King is checkmated.
I'm trying to figure out how it works for you. Let's say Black checkmate the white King while taking a white Pawn. Black says "checkmate", and White plays if, as you say, Black has to take a turn. So White plays while his King is checkmated. Either he plays another piece while leaving his King in check or he plays his King by placing it on a square where it is also in prise, as it was checkmated. Then, and only then, Black seizes the White King (so a black piece is now on the King's square) and White's Prince is becoming a King. Correct?
In such a case, it is strange that White plays while his King is checkmated.
Sorry, it is not clear for me yet.