Sword of War and Peace deals damage when its trigger resolves, the creature it is equipped to does not.

When a creature equipped with deals combat damage to a player, its ability will trigger. When this triggered ability resolves, the Sword's controller will gain life equal to the number of cards in his or her hand and the player that received combat damage will be dealt damage equal to the number of cards in his or her hand. The source of this ability and the damage is from the Sword itself, not the creature that the Sword is attached to. It doesn't matter if the sword is equipped to a creature

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