First, the database and table which exists:

USE dbname;
select * from Authentication;
+----+---------+--------------------+---------------+----------------------+
| id | userid  | password           | role          | email                |
+----+---------+--------------------+---------------+----------------------+
|  7 | user1   | ljkjkjhjhjdhfZn0mz | administrator | [email protected]       |
| 10 | user2   | gdgdgdgdgdg^4YU    | user          | [email protected]       |
| 11 | user3   | dsdsdsdsdsd8       | user          | [email protected]       |
+----+---------+--------------------+---------------+----------------------+

Now create the other table and its fields:

CREATE TABLE `Login` (
  `id` int(6) unsigned NOT NULL AUTO_INCREMENT,
  `TimeLoggedIn` text NOT NULL,
  PRIMARY KEY (`id`),
  KEY `id` (`id`),
  KEY `id_2` (`id`)
) ENGINE=InnoDB AUTO_INCREMENT=12 DEFAULT CHARSET=latin1;

Now duplicate the field id in Login and populate it with existing data from table Authentication.

INSERT INTO `Login` (`id`) SELECT `id` FROM `Authentication`;

Now create relation:

ALTER TABLE `Authentication` ADD FOREIGN KEY (`id`) REFERENCES `Login`(`id`) ON DELETE RESTRICT ON UPDATE RESTRICT;