Recently, this same issue was identified as the result of an installation being done as single user but the mailbox being copied in was from a multi-user installation. It just simply wouldn't work because of the way the v4.72 installer now handles single user.
Sine you're using the Win8.1 desktop to hold a copy of the Pegasus Mail installon the Win10 laptop I suggest starting from scratch as follows (conditional the the first statement below).
If, and ONLY if, your installation of Pegasus Mail on your Win10 laptop has program files in C:\PMAIL\PROGRAMS and the mailbox directory in C:\PMAIL\MAIL\ADMIN then I suggest you remove the current Pegasus Mail from your Win 8.1 desktop (renaming the PMAIL root directory to something like PMAIL_OLD will suffice for now, you can delete it once all is well). Now disable automatic mail download in the Win10 Pegasus Mail, shut it down, then copy the entire C:\PMAIL directory from the Win10 laptop to C:\PMAIL on the Win8.1 desktop.
If you want full Pegasus Mail functionality on the Win8.1 desktop, execute C:\PMAIL\PROGRAMS\WINPM-32.EXE, let Pegasus Mail load, then shut it down. This will create a registry entry of the current path of Pegasus Mail. Now run the Pegasus Mail installer as an upgrade (It will use the registry path created in the previous step) This installer will create the shortcut and appropriate registry entries for full functionality. If you don't need it, skip this step and just create a shortcut to winpm-23.exe. Enable/re-enable automatic mail download as appropriate.
You should now be able to replace the mailbox directory on the desktop with the one from the laptop until such time that the a configuration on the laptop breaks this (eg: adding a user).
IMPORTANT: I can't emphasize enough that this will NOT work if the paths to the program files and the mailbox directory are not identical on both machines.