Downloader service returns a Arthem uploaded file (FileInterface) in order to map it with your model.
use Arthem\Bundle\FileBundle\Model\FileInterface;
$fileDownloader = $container->get('arthem_file.file_downloader');
/** @var FileInterface $file */
$file = $fileDownloader->download('http://customwebsite.com/image.gif');
$myEntity->setFile($file);
$em->persist($myEntity);
$em->flush();