Have you looked at this firefox help link?

"How to retrieve bookmarks from a dead computer." https://support.mozilla.org/en-US/questions/1003872

There may be glitches when transferring a Firefox profile among computers, but it's worth a try. If necessary, you can always use the old files for a more selective restore.

Part 1

First, set Windows to show hidden files and folders:

https://support.microsoft.com/en-us/windows/view-hidden-files-and-folders-in-windows-97fbc472-c603-9d90-91d0-1166d1d9f4b5

Second, find the relevant profile folder on the old drive. For reference, I'll call it the "E" drive, but this would be whatever letter is assigned by Windows. Explore up

E:\Users\<username>\AppData\Roaming\Mozilla\Firefox\Profiles

That Profiles folder typically contains at least two subfolders whose names combine a random portion and a descriptive name like "default-release".

The immediate objective is to identify the most (recently) used profile. You can use the Last Modified dates and/or double-click into the bookmarkbackups folder to see whether it has up-to-date backups. The file creation dates are embedded into the file names, for example:

bookmarks-2024-11-22_2498_gibberish=.jsonlz4

Got it?

Part 2

The idea is to transplant the entire old profile folder (not Profiles, just the individual folder) into the same location on the new PC. Then you need to educate Firefox that it's there. The following post has the steps (with a different source folder):

https://support.mozilla.org/en-US/questions/1474421#answer-1687884

I want to promptly thank you for your prompt response although I am not able to try it just yet. I expect I can review and follow your guidance and hopefully and successfully succeed in making the important transfer. I will keep you posted likely within the next week. Thanks again.