It is possible to back up your emails using the features provided by Open-Xchange platform at https://privateemail.com. In order to back up a single email select it, click on three dashes icon and select Save asfile option. Email will be saved in .eml format to your computer:
NOTE: Only emails shown on the screen will be copied.
Importing emails to Private Email
In order to import emails to App Suite webmail select them and then drag-n-drop to the required folder.
NOTE: you can import only emails saved in .eml format.
Once the transfer is completed you will see all imported emails as unread ones and the corresponding message: