I don't think you can download the old messages(/emails).
If you wanna back up your old emails, you can try this. go to DH panel --> Mails --> Manage Mails:
Enable "will be delivered to these email addresses"
in the textbox, key in an email address. Note you should key in at least two email addresses. One is the one you want to forward the emails to. The other one is the same email address so that the server will forward a copy of email to the same email address.
For example, if the email address is email@example.com and the backup email address is firstname.lastname@example.org. Key in the two email addresses (note one per line)
Once you set up this, all the emails will be forwarded to you (outlook) and be copied to the email server.
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