So I changed this in the wp-config.php file:
define( 'AUTH_KEY', 'put your unique phrase here' );
define( 'SECURE_AUTH_KEY', 'put your unique phrase here' );
define( 'LOGGED_IN_KEY', 'put your unique phrase here' );
define( 'NONCE_KEY', 'put your unique phrase here' );
define( 'AUTH_SALT', 'put your unique phrase here' );
define( 'SECURE_AUTH_SALT', 'put your unique phrase here' );
define( 'LOGGED_IN_SALT', 'put your unique phrase here' );
define( 'NONCE_SALT', 'put your unique phrase here' );
And added all the hashes from the wp-config.php file on the live server and now it works.