I did it this way and it worked perfectly:

https://support.mozilla.org/en-US/kb/moving-thunderbird-data-to-a-new-computer

I got to item #7. I'm in my destination computer with my thumb drive plugged into the USB port. I bring up the contents and right click on Thunderbird file.

1. 8 says to open Thunderbird. How do I do that? This is a new installation - there is no Thunderbird to open.

I guess the logical assumption is that you first downloaded and installed Thunderbird on the new computer.

Thanks, Truman!

In Thunderbird your data is stored in your profile and is separate from the actual program files. The article that was linked above is how to move your profile with all your data in it.

Keep that in mind if you ever give away or sell a computer. If you just delete the Thunderbird program your data is intact in your profile. If the new owner installed Thunderbird your data will appear.