Using an update trigger to update another table
DELIMITER $$
DROP TRIGGER IF EXISTS after_update_A;

CREATE TRIGGER `after_update_A`

    AFTER UPDATE ON `A`  FOR EACH ROW
    BEGIN
        UPDATE TABLE B
        SET  username = NEW.username
           , password = NEW.password
           , email = NEW.email
        WHERE id = NEW.id
    END

    $$
DELIMITER ;

CREATE TRIGGER `after_update_A` AFTER UPDATE ON `A` FOR EACH ROW
BEGIN
    UPDATE TABLE B
    SET  username = NEW.username
       , password = NEW.password
       , email = NEW.email
    WHERE id = NEW.id;    //<<-----------
END $$