When you export the folder (right-click, IET NG/Export folder), you should have an mbox file with no extension (type File). If it's an IMAP folder, the mbox will contain the message contents if offline folders are downloaded (the default). To confirm the contents, import it to Local Folders (right-click, IET NG/Import mbox file). You can't import an mbox to an IMAP folder, but you can copy messages from Local Folders to IMAP folders in 'small' numbers at a time.

The message I get when I export from Thunderbird/ImportExport NG is: "You’re exporting the local copy of a IMAP or NEWS folder. The local folder could not have all the messages present in remote folder. Are you sure you want to continue?"

I run the export and end up with a 3 GB file (6333) messages) with no extension (type File).

When I try to import the file into Horde (using a new folder called "old email" it goes through all the motions. Says Uploading and takes about 15 minutes. But then I have no messages in that folder.

Despite what it says, uploading 3GB of mail in one step isn't going to work even in the best of circumstances. Try a few dozen messages at a time, copying from Local Folders, then increase it until it fails. Unless you desperately need the messages in an IMAP folder, just keep them in Local Folders.

Thanks, the person I'm helping (of a certain age) has saved every email she's gotten since 2011 and doesn't seem to understand what the delete key means.

I just moved the 2020 emails and that worked. Thanks, I think I've found a way forward.