What methods are there to forward all existing email from one Google Apps email account to another?
So this is not for future email, but all email currently in the box. These will be different Google Apps accounts.
Trying to do it within the web app will be very painful.
The way I would attack it would be to install an e-mail client that supports IMAP. (Thunderbird, perhaps.) Then set up both accounts in the e-mail client. Then, when they're all synced, use the client to copy all of the messages from one mailbox to the other.
You can delete the client software after that if you don't want to use it.