This would be easiest:
1.) Create a script (on the PHP server) that writes the dynamic information that is to be used on the remote server on the PHP server.
2.) Put that script in your crontab (update it however oftern you like)
3.) Install SSH on both servers and run ssh-keygen on the PHP server - put the contents of ~/.ssh/identity.pub into the ~/.ssh/authorized_keys of the non-PHP server (make sure it is one line!)
4.) after you run the script that generates the static html (with the dynamic content ;o) have your crontab scp the static html file over to your non-PHP server
This requires a few things:
1.) SSH on both servers (FTP might work also ...)
2.) a PHP binary somewhere on the PHP server
Hope this helps!