White mates in 3:
No such thing.
The explanation doesn't compute. Never heard of what you are proposing.
The answer involves uderpromoting to a rook and Castling with the new rook on e8 (the King has not moved, the e8 rook technically has not moved and no piece is intercepting the King's journey, so "0-0-0-0-0-0" is a 'legal move' here)
I beleive that FIDE added a rule that the king and castling rook must be on the same file. I did wonder at a puzzle like this one myself, though.
White mates in 3: