Gmail – How to export all emails between theself and another person from Gmail, i.e., to send to a third party as a readable file

Did you read the answers to your other question?

Per the link I gave in my answer to your other question:

If you absolutely need the old label structure, the only solution is to use an IMAP client to connect to both the old and new account and copy over folders/labels. But this solution can be tricky, because you can only copy over a certain (unspecified) amount of mail at a time. The non-Google program Gmail Backup might be able to assist with this process, but I can't vouch for its effectiveness.

Regarding contacts, from the same link:

Step 3: Export and import your contacts Login to the old account and follow the instructions on the Export Gmail contacts page. Remember the location of the saved file.

Login to the new account and follow the instructions on the Importing CSV files page using the file you just saved.

As a bit of a spoiler, we tested this last night. I have two email address (which I will call for the sake of example "test1@gmail.com" and "test2@gmail.com"), and then we did this:

To:      Rebecca <Recip@gmail.com>
From:    My Name <test1@gmail.com>
Subject: this is a test
Body:  blah blah whatever

and additionally

To:      Rebecca <Recip@gmail.com>
From:    My Name <test1@gmail.com>
Subject: this is a test
Body:  this should nest under the other

and voila, they nested. No work required. And then we did this:

To:      Rebecca <Recip@gmail.com>
From:    My Name <test2@gmail.com>
Subject: this is a test
Body:  does this nest with the others?

And it didn't nest!

So in other words, two emails from the same sender with the same subject will nest. Two emails from two different addresses with the same subject will not nest.