Google-drive – How to transfer documents from Google Apps to another Google Account outside of that organization

The e-mail fetcher would only fetch new e-mails that are on the inbox of the POP account.

IMAP is the the way to go. Here's a quote from another guide:

It was simple: I merely added Gmail as an IMAP account to my Apple Mail client, then just dragged folder-by-folder all the messages important to me onto my Gmail account. It took a while to transfer all the messages (be sure to open the Activity window in Mail to see your progress), but once it was done, all my old messages were safely stored in Gmail and had their original dates! Perfect!

Unfortunately, there's no completely automated approach to this. Either you or your users will need to follow this approach:

1. "Re-name" all of the users on the domain you want to migrate. Re-naming actually gives you the option to change which domain a user account is part of. See Google Help Article.
2. Once you've moved all the users to your main domain, you can delete that domain from the original (temporary) google Apps account. Because none of the users have been deleted, all of their email, calendar, docs, etc. will still exist in that account.
3. Create the new Google Apps account with that domain name
4. Create user accounts for all of those users in the new Google Apps account
5. Use Gmail-Backup to backup all of the users' emails, and then use the same tool to restore those emails (together with all labels) to their new account. If you're doing this yourself, you'll need to temporarily set all of the users passwords to something you have access to.
6. If necessary, you can also log in to each of those user accounts and export their mail filters and then re-import them on their new accounts.
7. Go into calendar settings in each users Google Calendar account, and "share" each of the users calendars with their new account. Give them access to "make changes and manage sharing". If this doesn't work, it's probably because your current Google Apps account has the calendar settings too restrictive, you need to be able to share calendars with users outside this organization (namely your new Google Apps account)
8. Go into Google Docs for each user, and go to "All Items" under "More" on the left. Scroll to the bottom and make sure that all items have finished loading. Then select all docs using the checkbox at the top left and then select "sharing". Share all of these Google Docs with the users new account. Again, you may encounter restrictions from your original domain that you have to remove. You also may encounter issues sharing documents that were originally shared with this user by someone else. In that case you may have to share all of that users' own Google Docs with their new account, and then handle individually the items that were shared with them by others.

There is (unfortunately) no other way that I know of to transfer an account from one Google Apps domain to another. Although there are many steps here, it's not a very big job unless you have many users.