Keeping saved mail when deleting an email account

I want to switch my mail from a POP account to an IMAP one. I need to understand though what happens to mail from the old account that I have saved in folders 'on my Mac'. If I delete the POP account will the saved emails still be accessible? Also, how do I make sure that I still have access to mail in the sent and trash folders of the old account?

Thanks in advance for help. It's vital to me that I don't lose access to my saved items.