another possible way to do this is by uploading this file to your website.com site and use CURL to send the image to another server. once this completes you can remove the image again.
see CURL PHP send image for more information.
-- UPDATE --
For SSH connection you need to install additional libraries in order to allow php to make SSH connection. an excellent tutorial can be found here.
-- UPDATE 2 --
The question intrigued me, so i expanded my research. there seems to be another PHP Library phpseclib around on Sourceforge. In the documentation on page 5 there is some information on how it works.
The only good way to make this to work is to read the image to binary, and send it over the the other server, as text and write that into an file, hence creating an image from the source of the original.
Also place the image in a public folder that is accepts calls from your website1 domain, this way you also prevent hot linking your images and saves considerable data.
I also came across this for help with phpseclib.
in the end i wouldnt choose for a solution like this. I would swap your website from server1 to server2, just to keep everything in one place.