How to change the hosting company and keep the email messages?

Question

We aren't pleased with our current shared hosting account and we will change our hosting company to AWS (if this matter). The main problem which I see now is that we have two email accounts (let's say a1@example.com and a2@example.com) which have a lot of messages on the old IMAP server.

How can we save the messages from there? Ideally how can we have the messages on the new server? (There is an \email folder in \public_html but I don't know how to use it).

Yes, I read this question but the answer imply a manual download of each message which isn't suitable in our case due of the number of messages.

Edit:
Old Host> Linux cloud shared hosting + cPanel (we use there RoudCube/Horde/Squiremail) New Host> AWS Linux hosting

We are ok with any webmail interface (prefered RoundCube). We try to avoid a local client (Outlook/Thunderbird etc.) because we want to have the emails accessible from everywhere.

Answer 1

My own answer - perhaps is useful for someone:

First be sure that you have the same accounts on the old and new server.

Second, look at /home/$username/Mail on the old host and see if there are some files there.

If they are then you must find what format they are by looking at the directory structure (maildir or mbox). Do the same for the new host in order to find what format the IMAP server expects. If the structure is the same, then you can simply copy to the new hosting in the same structure and the messages will simply pop up in your inbox.

More details at https://rimuhosting.com/knowledgebase/linux/mail/migrating-imap-accounts

Answer 2

Upload everything on new server, then during the weekend, change DNS and MX entries. That's the best solution for this, and that's the way it's done, but still, the clients should be able to access to old e-mail until DNS is propagated.

You can not transfer messages to the new server unless you download them, and reupload them. If your client doesn't use mail client, you need to do that. There's no other solution.

Or... best solution is to convince your client to use mail client such as outlook or thunderbird. :)