file_put_contents

<?php
$url = 'https://external.xx.fbcdn.net/safe_image.php?d=AQAxiUtD3ARM7k63&url=http%3A%2F%2Fs.ndimg.de%2Fimage_gallery%2Fnew_netdoktor%2F09%2Ffotolia-63049294-drubig-photo-fotolia-com-800_id_81735_257409.jpg';
//note will rename image after transfer, dir must exist.
$img = 'images/facebook/YourImageName.jpg';
// allow_url_fopen = on "must be on in php.ini or php5.ini"
file_put_contents($img, file_get_contents($url));
echo '<img src="'.$img.'" />';
?>