The default setup of Horde is mark messages as deleted when you delete an email. The email will still remain in the folder, greyed out and strikethrough. To move deleted emails to Trash, click on the cogwheel > Preferences > Mail.
Click on Deleting and Moving Messages.
Tick the box beside “Move deleted messages …” and click Save.
Additional options will be shown after you saved. The default folder to move deleted emails is Trash, and Purge is set to Never. You can change the folder and the frequency of the purge as you wish. Click Save when you are done.
Note: Ignore settings with (Basic view only) because basic view is no longer available.
Deleting an email in Horde will automatically move the message to the “Trash” folder once you enable this option. Note that previous messages you deleted will need to be moved to the Trash folder, or “deleted” again, if you want to see those messages removed from the inbox.