Conversion while keeping mail intact

Is there a way to remove and replace an account so that we do not have to lose the current emails? I am in the unenviable position of moving my emails to third party servers because the ISP is no longer offer it, I need to update the 2 acc from PO3 to IMAP for the new servers to deliver mail. If I click the delete account in EMclient to removes everything and I want to keep the mail.Not to mention all the contacts in EM Cliebnt. I know that you cannot convert the current settings from POP3 to IMAP without adding a new account.