I suggest first install Thunderbird so that the appropriate profile folder is created (.thunderbird). Then, exit Thunderbird and copy the desired profile to overlay the default at the .thunderbird folder.

@david It's my understanding that MX Linux comes with Thunderbird installed. Should I do something more to have it installed properly, such as ensuring that the same version is on the external drive and the new install? After that, should copying the profile from my laptop to my desktop computer bring all the folders with it? I thought that was what I did when I upgraded to the OS I have on the desktop now. I entered the username and password for my TB account, and it opened with my profile with the same information as before, but there were no email accounts. I had to add them, one at a time, before I could see everything in my inboxes, etc. Maybe I don't understand what creating the appropriate profile folder, and overlaying the default, mean. Do you know of somewhere I can read step-by-step instructions for exactly how to do this? Thank you.