I have been trying for some time now to get the uddeIM component for Joomla 2.x/3.x to work correctly in HTTPS, but it simply does not display right and the CSS styles are lost. This can be reproduced on stock Joomla install with no third-party extensions and default templates. There is something wrong in the extension causing mixed content (HTTP) when using HTTPS. This is undesirable.
Visitors of a website do not understand that private messages have the possibility to be encrypted with this extension on the server side. So to visitors, they may believe the private messages are not secure. It is important that this extension be fixed to allow websites to run with HTTP or HTTPS and encryption for messages on or off.