Hmm, which Mozilla folder? It needs to be from this hidden folder path:

C:\Users\<username>\AppData\Roaming\Mozilla\Firefox

To set Windows to show all hidden files and folders, see: https://support.microsoft.com/en-us/windows/show-hidden-files-0320fe58-0117-fd59-6851-9b7f9840fdb2

To get that set up on your new computer:

Could you try the transplant method described in the following thread -- note that your source folder will be your flash drive instead of a C:\Windows.old folder:

https://support.mozilla.org/questions/1321847

Note that you need to register a profile in profiles.ini to make Firefox recognize this profile.

You can find the profiles.ini file in a hidden location:

• Windows: %AppData%\Mozilla\Firefox\
  C:\Users\<user>\AppData\Roaming\Mozilla\Firefox\
• Mac: ~/Library/Application Support/Firefox/
• Linux: ~/.mozilla/firefox/

You can recover an unregistered profile via these steps:

• use the Profile Manager to create a new profile
  https://support.mozilla.org/en-US/kb/profile-manager-create-and-remove-firefox-profiles
• click "Choose Folder" in the Profile Manager
• browse to the location of this profile to register this profile in the Profile Manager and use this profile

See "Profile was moved or renamed":

• https://support.mozilla.org/en-US/kb/how-run-firefox-when-profile-missing-inaccessible

Note you should never use "Choose Folder" to specify a folder that already contains files and that isn't a Firefox profile folder. Only use "Choose Folder" to recover an profile that isn't listed in the Profile Manager.