I’ve had this same error, I don’t know what’s causing it (the plugin uses a wordpress function to download, and that one fails, so it’s not really their fault), but there’s an easy fix.
Download the zip file from the original server to the uploads/wp-clone folder on your new host (e.g. /var/www/wordpress/wp-content/uploads/wp-clone/mybackup.zip). Then instead of specifying a URL in the restore box, enter the path to the zip file (I think the file name is enough already). The plugin will first check the local upload folder for a file with that name, and since you’ve downloaded it there it’ll restore your site from that file.
