.....is extremely relevant here. Doubtless moonraker, and various other Puppy users on here will agree with me; for those of us who are 'proficient', there are a ton of different ways to get a launcher for Palemoon.That depends how proficient the OP is on Linux.
Pup uses the JWM/ROX-filer 'pinboard' combo. You can drag the executable directly to the 'pinboard' (desktop icon grid), tart it up with an icon, and there's your launcher. A recent feature in newer Puppies allows you to place a launcher in the Menu with 3-4 GUI clicks. Ditto for placing one in the 'Quick Launch' area. You can place custom launcher scripts in /root/my-applications/bin, /usr/bin, /usr/sbin/, usr/local/bin.....reference any of these from the Menu, the Quick Launch area (or drag-to-desktop).....honestly, the list is endless.
I, personally, run a single instance of the current Palemoon from a remote, auto-mounted partition, and have custom MenuEntry packages which I simply click-to-install whenever I set-up a new Puppy.
Many, many ways to achieve the same outcome, though there's no getting away from the fact that Pup's 'run-as-root' user model makes doing so much of this kind of thing very much easier than more 'mainstream' distros.....