There's no simple way to do that.

I'd consider copying the working profile to the new computer then simply delete the unwanted accounts. Would it matter that your other accounts would be copied to the new machine? Is there a security/privacy concern here?

Alternatively...

In principle, if you set up the account on the new machine, you could copy over the corresponding files from the old profile and paste them into the appropriate part of the profile on the new computer. You do this at file system level, using (for instance) Windows Explorer, not within Thunderbird itself.

Is this a transfer of a working account, or more for archive/reference purposes? In the latter case moving the copy into Local Folders can be useful, and safer than tampering with a working account.

Or move the profile extract into Local Folders in the file manager then move the messages, in Thunderbird this time, to appropriate folders.

https://support.mozilla.org/en-US/kb/profiles-where-thunderbird-stores-user-data

Thank you for you detailed answer. I am not surprised that there is no easy answer as I appreciate the complexity of the profile. I am thinking to do a wholesale profile transfer and subsequent deletion of all but one of the accounts as you suggest. Again, thank you very much for your helpful response!

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