So I am guessing you want a live update for your client, where he makes the corrections he wants on his website and it automatically overwrites the html file on his apache server? One thing is you can map a network path to the specific file from his PC? Are you inquiring more of a program that does that for him? I know there are some gui fronted web apps for Linux servers (http://www.webmin.com)where he can upload his most recent page instead of doing everything from the comand line. Hope that is the answer your looking for, have to do some research.

To accomplish you goal you can setup the client with ssh or ftp access to the server (you will need to properly secure those ports) and can redevelop the site to be css based to make implementing changes easy. The alternate option which the other have recommended is to set the site up on a cms system so it can be easily updated from within the active pages by authorized users.

I think the question is not complete. But I guess u need a CMS. I would recommend you using Silverstripe. Its powerfull and very well designed.

http://www.silverstripe.org/