We changed recently our Hosting provider. How can we remove the old IMAP account in Apple Mail without loosing any Mails and have them uploaded to the new server including all IMAP folders?
You can probably also do this directly (old IMAP to new IMAP) but I run into IMAP implementations in the past which weren't too stable during batch copying. So keeping a local copy (at least for a short time) is recommended.
If a local copy is not possible due to mailbox size, you can alternatively try to copy old IMAP to new iMAP folder by folder. Be sure to verify each step at least visually.