At the end I found a solution:
add_action( 'admin_head-post-new.php', 'cuar_owner_required' );
function cuar_owner_required()
{
global $current_screen;
// If not our post type, do nothing
if( 'cuar_private_file' != $current_screen->post_type )
// return;
?>
<script language="javascript" type="text/javascript">
jQuery(document).ready(function($)
{
// Tick the checkboxes of categories 3 and 9
$('#cuar_owner_select_usr').attr('required','true');
});
</script>
<?php
}