Hello,

It looks like your old profile folder is not recognized, since you see new content as if it would be a new install (due to the whatsnew and welcome screen). Often this is a matter of making the profiles.ini file in the /Profiles folder (parent of the actual profiles folder) match the actual profile folders you moved from another system. New profiles can and most likely will be named differently than any copy of another profile.

Did you have a look at the Back up and restore information in Firefox profiles and Recover important data from an old profile support articles? There would be 2 approaches: either overwrite all content (files and subfolders) of the newly created profile, or just the sessionbackup files from it, depending on what else you may find important to keep. See here for more info about files in the profile.

There have been recent changes to some file (around Firefox 55), but that should not be an issue as long as you keep version 49 for the new install. There should be no difference between 32-bit and 64-bit systems with regard to storing tabs/sessions either.

Do note that restoring sessionstore files can be tricky - perhaps this question provides more insights about that. Personally however I cannot recall session history to be gone after copying or moving profile info, requiring to use other files than the existing ones from the old profile.

...I got it working (EDIT: the above articles were quite informative). For future reference, here is what I did:

Shut down Firefox on the WinXP machine. On the Windows 7 solid state drive, I went to this folder:

\Users\mike\AppData\Roaming\Mozilla\Firefox\Profiles\profile.default

and copied the file "sessionstore.js" to this location on the Win XP machine:

\Documents and Settings\Administrator\Application Data\Mozilla\Firefox\Profiles\profile.default

The last date of "sessionstore.js" from the Windows 7 SSD is about 7 weeks before the motherboard died. I probably opened and closed more tabs during those last 7 weeks, so this is not a complete recovery. But it is much better than nothing.

A few notes:

(1) On the Windows 7 machine (before about Firefox 55) there are two different places where your profile is the name of a directory (for me it was e6zus848.default). Make sure you navigate to the correct directory.

(2) sessionstore-backups is the name of a directory. That's not where the sessionstore.js file is. The Windows built-in file search function can find the file if you are confused, like I was. Just check the box to show hidden files, system folders and the like before the search begins.

(3) Please use add-ons, tab groups, or other methods to preserve tabs, bookmarks, and so forth to prevent this kind of disaster from happening again (there appears to be some sort of Firefox login that synchronizes tabs across devices).

I'm marking this as solved.