If you have already enabled the mail archiving feature in the tweak setting (see below) then you should be able to access the archived emails from Webmail, but you need to first subscribe to the new archive folders before you are able to see the archived emails in the "Archive" mailbox interface in Webmail.
Here is how you can confirm if the Email Archiving support has been enabled:
grep -Ei mailarchive /var/cpanel/cpanel.config
emailarchive=1
Here is how you can subscribe to the new folders:
1. Log in to cPanel
2. Navigate to Archive in Email >> Archive
3- in the search box under the "Manage Archiving" interface search for your domain
4. To the right under Actions Select Access Webmail
5. Enter Roundcube Webmail
6. Click Settings from the left panel
7. Click Folders
8. And then utilize the toggle option to the right of each folder to (un)subscribe to that folder