You log in sync on Firefox on the other computer with the same sync account and let it connect to sync again. Because the nature of Firefox sync you need to leave both system running for the process of sync to sync from the old computer to the new computer to match the sync. Shutting one off doesn't guarantee it will sync correctly the data so keeping both one is what you should do to insure it works. Firefox has a sync option you need to click the 3 bars and sign to sync.

Thank you so much for your very nice reply!! I have two thoughts: first, during the initial sync process, ALL of the tabs were indeed synced between the two computers (...and I never logged out if Firefox in either of them). I was under the (wrong?) impression that once fully synced, my new computer's Firefox would retain the synced tabs in its memory. Secondly, I no longer have the second computer! (...I traded it in) -- so, it seems like for some reason (or maybe it was never designed to do this?, which would be unfortunate), the sync setting did not "capture" theold computer's tabs and hold on to them. I realize this is not the real definition of "sync," but I thought this would be a common enough usage of the "sync" function that the overall process might work this way. I guess I am out of luck!?!? Thank you again.

At that point if you sync that would mean that data would be gone since you don't have the old computer that had the data. This is why one should do the Firefox profile/bookmark/session data backup sync isn't a "backup" option only sync data with another Firefox sync login.

Thank you very much for your assistance.