It might be possible with a bit of extra work with other software. Here's one example, not the only possibility.
a) Set up your Boss with a Free drop box account
b) Have FileMaker server save a back up copy to a folder inside the drop box folder
That puts a copy where he can find it, but it put's it in a folder with the days date as part of the folder so he won't be able to set up a short cut to it.
You could also use a system script such as a batch file or VBscript to copy such a back up file to a folder inside of drop box. The script can use the day's date to adjust its file path to the correct current back up copy and now the file is always accessible in the same folder inside of Drop Box. This would make it possible to set up a short cut that your boss can double click on his desktop to open the file.
Just make sure that your boss knows that any changes he makes won't appear in your hosted copy.
Thank you so much for the advice, much appreciated Phil,