This is a really really really big security risk, because you're giving the admin of the other server ability to execute code on your server. You probably don't want to do this.
include() or require() will execute PHP code in the remote file. If that's a .php file, it will only execute it if PHP generates further PHP, which the manager of the remote server could easily achieve.
Instead, you should read the file in and output its contents, that's much safer.
It might be advisable to cache a local copy of the file too, in case the remote server is unavailable, and to increase speed.
In order to fix up the image URLs, you must also have the images on your local server, as the page is using relative (or root-relative) links for their images. This is reasonable.
Alternatively, parse the HTML (for example using DOM parseHTML) and rewrite the links as absolute. This is not easy.
I take it you have the permission of the content authors on the remove site? Can you not simply ask them to make another version of the page which uses absolute image URLs?
Mark