Complementary answer for Google Documents
I had a lot of Google documents to migrate from a free account to a Google Apps academic account. The best way I found was using the Google Drive Desktop (PC or Mac) to make the copies. Here are the steps:
- Google Drive Web:
- In the free account, share the documents with the Google Apps academic user
- In the academic user account, move the "Shared with me" files/collections into your main list (or use the Add to My Drive button). More info To make it easy, you can create a collection called "Files to migrate" and organize the things in there. This is so the shared stuff from the free account will show up on your PC/Mac.
- Google Drive Desktop (Download info)
- Set up Google Drive Desktop for the destination (e.g., Google Apps paid) account.
- If all goes well, you should see the "Files to migrate" collection in the Google Drive folder on your PC (or Mac)
- Using your Desktop interface, copy/paste the "Files to migrate" collection. The new files should belong now to your Google Apps academic account. This make take some time.
Credit goes to Bibiano Wenceslao, who wrote a blog post on this, although it was not specific to data migration.
Note: I didn't test it on a Mac - I used the Windows 7 PC version of Google Drive Desktop.