Re: old emails
No idea. It depends whether Verizon will upload them into AOL for you. Aqua Mail won't.
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Re: delete account
Yes you will need to remove the account from Aqua Mail and add it back.
I would say that there is no real need to
remove the "old" account, is there?
As a matter of fact, if Verizon does not migrate the old messages to the AOL servers, I would suggest keeping the "old" account in Aquamail, just turning off all syncing. This would be the way to keep the old messages (downloaded via POP3) on the phone.
@Jaffeb: From what I've read, it sounds to me (although I haven't seen it written explicitly), that the messages will be migrated. But if I were you, I'd take my own measures to make sure they are preserved.
Just in case Verizon will not migrate old messages to the new server, - the route of migrating them that I'd investigate is to use some other program for migration.
E.g., I've used Thunderbird for migrating messages from one account to another -- but both were accessible via IMAP.
I haven't used Thunderbird with POP3, but I'd expect the same can be done, as long as the "new" account is accessed via IMAP (i.e. migration from POP3 to IMAP should be possible).
Add a POP3 account in Thunderbird (while you still have access to the old server). Make sure that you configure "keep messages on the server"!
Download the messages. Then, when you can access the new, IMAP server, - add that as an account in Thunderbird.
(Keep them separate, which is the default option.)
To copy messages, using the mouse, choose the Inbox folder in the first account and drag it to the other account, and drop it onto that account (all in the left panel). That should start copying messages from one account to the other. Once the messages are in the new account (via IMAP) and fully synced to the server, they should be accessible in your new account in Aquamail.