I cannot speak knowledgeably or correctly about a POP3 to IMAP conversion, so I won’t try. However, I have the setting on K9 (running on a Chromebook, not a phone) to always (unless I blank out the field) Bcc: myself (I actually use Cc: to myself) to I get a copy in my Inbox, which I can leave on the server or delete as I choose. That way I don’t have to worry about recovering sent messages.