PHP - Save hosted image?

I’m thinking of making a dynamic flash page that allows users to upload their own images for interacting with in the swf. But I’m thinking it would nice to allow for using hosted images as well as local images.

See w3c validator site for an idea of the kind of thing I’m after: http://validator.w3.org/

So, ignoring the whole flash side of things, I need to be able to save the user chosen image to a specified location on my server. Using the normal PHP methods I can achieve this for uploading of local files. But my questions is, is it possible to save a copy of an image to my server, given the address of that image on someone elses server?