thank you for your reply
the problem was cookies, I had to add these lines of code in the wp-config.php for the connection to work properly on all sites multisite:
// Cookies
define( ‘COOKIEHASH’, md5( ‘annaml.com’ ) );
define( ‘COOKIE_DOMAIN’, ‘annaml.com’ );
define( ‘ADMIN_COOKIE_PATH’, ‘/’ );
define( ‘COOKIEPATH’, ‘/’ );
define( ‘SITECOOKIEPATH’, ‘/’ );
define( ‘TEST_COOKIE’, ‘thing_test_cookie’ );
define( ‘AUTH_COOKIE’, ‘thing_’ . COOKIEHASH );
define( ‘USER_COOKIE’, ‘thing_user_’ . COOKIEHASH );
define( ‘PASS_COOKIE’, ‘thing_pass_’ . COOKIEHASH );
define( ‘SECURE_AUTH_COOKIE’, ‘thing_sec_’ . COOKIEHASH );
define( ‘LOGGED_IN_COOKIE’, ‘thing_logged_in’ . COOKIEHASH );