One way to make sure you have everything that is on a web site is to import the site to your PC. When in Front Page, click on File, then Import, and then From Web. You need to enter the URL at this point and finish. Front Page will import the entire web site. As far as I know Front Page does not let you pick and choose the files you want to import, you need to do the entire site.
If you have FTP access, and a program like WS_FTP, you can just copy the files with that. If your business partner can email you an exact list of what changes he made, including images and layout changes, you can use an ftp program to copy these to your PC.
Two people updating a website from two different locations can present problems if you are updating the same pages. It doesn't matter if you are next door to each other, or half way around the world, making sure you both are always up to date can be tricky. I've been there. Sometimes a change made on a page will also affect a file in the border, derived, or overlay folder. Simply copying the altered page to your PC may not get everything.
If you are working on two different sections of your site, it might be a good idea to make a sub-web for one of the sections, where each of you has your own set of folders on the web.
Jon Holmen