I’ve used this on my Windows 7 machine and it will export the list to a registry file directly onto your desktop. Copy and run this as-is, do not change anything to include SimonTatham. If you change it, it will not work.
regedit /e "%userprofile%\desktop\putty-sessions.reg" KEY_CURRENT_USER\Software\SimonTatham\PuTTY\Sessions
The above command did NOT work on my Windows 10 system but the following DID work on Windows 10 and Windows 7:
regedit /e "%userprofile%\desktop\putty.reg" HKEY_CURRENT_USER\Software\SimonTatham
Once the file has been created, you can move it to other systems. As a reminder, if you are using SSH keys, those will need to be copied to the other machine(s) as well.
To “import” the list of PUTTY sessions, just double-click on the file. Open PUTTY and you should see your saved sessions.