media_handle_sideload on a file already on server

I solved this by simulating a $_FILES array:

$file_array = array(
            'name' => basename( $file_path ),
            'type' => $url_type,
            'tmp_name' => $file_path,
            'error' => 0,
            'size' => filesize( $file_path )
        );

And then

$att_id = media_handle_sideload( $file_array, $post_id );

As simple as this..