@xenial :-
'Kay... Yes, it can be done.....depending on what you're trying to do. I assume - by what you're asking - that what you want to do is to save "your" desktop set-up "as-is".....yes?
To the best of my knowledge, the exact file that actually controls all this is the PuppyPin file, at /root/Choices/ROX-Filer/PuppyPin. This is what records - in real-time - the exact positioning of every icon (down to the individual X-Y pixel co-ordinates), what that icon is, where it's being read from, what executable action it controls, what background wallpaper you're using (and where it's being read from), etc, etc. And it's ROX that controls this BTW, not JWM.
ROX controls the actual desktop, because the grid where you locate the icons on the desktop is in fact a ROX-Filer 'pinboard'.....so in that respect it's an extension of the file-manager. This gives the ability to 'link' to other items in ROX, and this is, of course, what enables the drag'n'drop functionality of the Puppy "desktop".
JWM, on the other hand, controls things like the appearance/layout of the 'tray' at the bottom or top, and from that it follows that JWM also controls the appearance of the Menu.....though it is of course linked to ROX to make it actually execute anything.
Wallpaper selection is controlled by resources at /usr/share/backgrounds, and the switcher script is usually at /usr/bin/wallpaper.
Icon selection, mm.....never used this one myself, 'cos it would never work with MY setups, so not sure where icon themes are located - but are usually administered via the script at /usr/sbin/icon_switcher, along with the theme being recorded at /etc/desktop_icon_theme. (EDIT:- /usr/local/lib/X11/themes, it seems).
It's a wee bit more inter-connected than you might think. You have to remember, Puppy's "desktop" is not a 'single-entity' DE, like most distros.....it's a combo of multiple items, each chosen for their lightness & ability to work well together.
So, again; what exactly is it that you want to do? A little more "flesh on the bones" would be good....
You can save this config stuff externally - outside of Puppy completely - followed by linking it back-in to the appropriate location. This way, it's NOT dependent on any form of Puppy 'save' behaviour at all, since it's in a 'permanent' external location (untouched by canine paws!)
Is any of this making sense?

Mike. 