Doing this is a level of frustration even if you have a Japanese friend help you. I wanted to transfer money from my post office account into my Mizuho account. I was at the Mizuho ATM. Big mistake!!!! Money was transferred out of Mizuho into the Post office account.
I then went to the post office ATM, and tried reversing the process. My money is now stuck in limbo somewhere until they decide to update their records. I'm hoping everything will be straighten out in a day or so.
FYI, you can only do this via the Japanese menus. They don't offer it under any English menu.