In RoundCube web mail you can archive old email into separate folders.
- To start, create a new folder to hold your archives: go to Settings, Folders and click the "+" button to add a folder. Give the folder a name, for example "Archive", and click save.
- Next, set this folder as the special folder for archiving email: while still in Settings, select Preferences and Special Folders. Select your new folder from the drop-down for "Archive" and select the way you'd like your archives organized (compatible with Thunderbird desktop email, or one folder per year or per month, or organized into Inbox/Drafts/etc., or by sender email address). Then click save.
When you go back to "Mail", you should now see an "Archive" button in the menu. Click that to archive the email you are reading.