I am changing my IMAP host and need Outlook backed up and configured correctly

Description of support work: My business has 3 custom email addresses on our website domain, e.g. aron@example.com, where example.com is our business website domain. Now we are about to change hosting providers from our old host to 1&1.

However before we change the name servers with our domain's registrar I need to ensure that I do not lose the use of any of the 3 email addresses we have. We currently access all 3 addresses from Outlook 2013 via IMAP. We need to ensure that after the domain transfer to the new host is complete that all our old emails are back on Outlook and that we can send and receive emails as we did before the transfer.

The initial backups and name server changes should be carried out on this Thursday night 30th April, and then backup and entering the new IMAP details into Outlook should be carried out the following Sunday morning 3rd April - once the DNS changes should hopefully have propagated. We need to do it over the weekend so that the disruption in emails is absolutely minimal.
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This will involve the following:

On Thursday night at 8pm:
- Remotely access 2 computers to back up all emails for 3 addresses from Outlook. Chrome Remote Desktop would probably be best.
- Enter the new name servers at the domain registrar.

On Sunday at 9am:
- Backup all Outlook accounts again in case any emails arrived since Thursday.
- Add the new IMAP details into Outlook for the 2 computers.
- Restore all emails and folders to the new email addresses, ensuring that sending and receiving from the new details work properly.
Extra notes: It is important that you are familiar both with DNS administration and knowledgeable in the use of Outlook 2013.