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A Palm OS emulator would be your best bet for getting the game running on PC. In addition to the emulator and game file, you'll also need a compatible ROM for the device you are emulating. There are links on the subreddit to downloading one and getting set up. If you have an Android phone, you can also use PHEM.
Additionally, Mummy Maze was ported to other platforms besides Palm OS (including PC), so if all else fails, you might have luck finding a version designed to run natively on your PC and going from there.
If you're on Android, you could use a Palm emulator like PHEM and just load the original .prc file.
Even if PHEM is no longer listed in the Play Store search results, you might still be able to install it by going directly to its listing link, assuming you're logged into the Google account that originally purchased it. It still shows up and installs for me here: https://play.google.com/store/apps/details?id=com.perpendox.phem
Ah, yes these tools would require a PC of some sort. If you have Android you could also try this emulator https://play.google.com/store/apps/details?id=com.perpendox.phem&hl=en_US
Feel free to share the backup, we spelunk palm files all the time.
There's a decent Android Palm emulator that can display skins of a bunch of different devices based on the Palm ROM you choose, or you can run stuff fullscreen, but still keep the greenish/grayish screen effect
There's an app called PHEM that allows you to run Palm OS in an emulator. It's pretty rad for a trip of nostalgia.
Palm emulator for Android:
https://play.google.com/store/apps/details?id=com.perpendox.phem
Got a Palm OS emulator on my Note 4 and it's awesome. Also works well with my S-Pen.
https://play.google.com/store/apps/details?id=com.perpendox.phem