This is actually a common manoeuvre in checkmates with pieces that cannot triangulate (e.g. Knight + Camel). Often you cannot afford to triangulate with your King, because that would give the bare King the room to triangulate as well, thereby cancelling the effect. In Alice Chess no piece can truly triangulate, because they must alternate between the boards.
But I suppose there is a way around that when checkmating a bare King, as in that case it doesn't really matter on what board the King is: the bare King can never approach it without either moving into check or through it, both of which is forbidden. So you can treat it like the King is always on both boards.
This is actually a common manoeuvre in checkmates with pieces that cannot triangulate (e.g. Knight + Camel). Often you cannot afford to triangulate with your King, because that would give the bare King the room to triangulate as well, thereby cancelling the effect. In Alice Chess no piece can truly triangulate, because they must alternate between the boards.
But I suppose there is a way around that when checkmating a bare King, as in that case it doesn't really matter on what board the King is: the bare King can never approach it without either moving into check or through it, both of which is forbidden. So you can treat it like the King is always on both boards.