Mail account full: Move and keep old messages on another device?

Moving the messages into a backup dir should work (I assume you are not using a Chatmail account). If you were using encryption and want to read them forever you will also need the decryption keys. The GUI key export was removed around 1.10, but you can hack into the Deltachat database and extract the private keys. Maybe test by copying a few e-mails first.

Is this the info you wanted? Deltachat does not yet really have much by way of archiving capabilities (“Archive Chat” just reorganises the display).