Hosting transfer, want to keep old mail, dont want to get prompt every 10 secs that old acc cant login to mail server

Hello, can someone help me with this please? Hosting transfer so I have new mail info, want to keep old mail acc in emclient for keeping history of important mails and conversations but dont wanna get prompt every 10 seconds that the old account cant reach the server and log in, can someone help with how to do this? Can I merge accounts somehow or just keep the mails without keeping the account?

You could just move the emails from the old account folders to the new one, and then delete the old account. Or you could create a set of local folders, and move the emails from the old account to those.

Always make a backup before doing anything drastic.

I dont know what means move easily. I have hundreds of mails there and when I try to move the folders with some settings I found it says cant connect to SMTP, you cant move special folder etc…