I’m not a member of both groups, however I’ve been working around that limitation by using this code in my functions.php. It was working until the latest update:

// Allow front end messages pro users to send messages to group they are not in
add_filter( ‘fep_get_user_groups’, function( $user_groups, $user_id ){
$groups = fep_get_option(‘gm_groups’, array());
if( $groups && is_array( $groups) ){
foreach ( $groups as $group ) {
$user_groups[ $group[‘slug’] ] = $group[‘name’];
}
}
return $user_groups;
}, 10, 2);