Connected Passers Do Beat an Opposite-Coloured Bishop

Every endgame book teaches that opposite-coloured bishops draw. It is the most useful rule in endgame play and it is also the one that costs the most points, because the exceptions are concrete and this is one of them.

Push the right pawn. e7 wins, f7+ draws. The pawn to push is the one whose promotion square your own bishop can reach: e8 is light, and your bishop is light-squared.

Do not promote too early. e8=Q+ at the wrong moment is met by Kxe8. Bb5+ first, both to drive the king away and to put the bishop on the diagonal that guards e8.

The colour is the whole story. The defending bishop is dark-squared. It can harass the pawns, but it can never stand on e8, so once your bishop covers that square the pawn is unstoppable.

The companion is a draw. Our position "Guard e6, But From the Right Square" is this same material one rank lower, and there Black holds. Two connected passers on the fifth are not the same animal as two on the sixth.