If what you're seeing is an image that says "Unsafe Image Removed" (or something similar), then that is because SquirrelMail will only show images in HTML Mail if the image is included in the message. That is, the image has to be like this:
This was one of the reasons I was reporting this bug in the first place.
Images that are not included in the image (whose src is a url to an external server) are considered "unsafe" images.
You can use another plug-in called Unsafe Image Rules http://www.squirrelmail.org/plugin_view.php?id=98
to allow users to define rules for which messages showing these external images are allowed or they can turn off the blocking of these images all together. Most mail clients have a feature to supress HTML images that are not included in the body of the messages, for example in Apple's Mail.app, the preference setting "Display remote images in HTML messages"
For whatever reason (security would be my guess), SquirrelMail developers decided not to show these images, but you can still install the plugin.
Unless I'm totally confused on what you're asking, then this certainly doesn't sound like a hMailServer problem (though I've been wrong before).
Two last things you can check to help you determine where the problem is, if a problem there be:
The first is a plugin called "message_details" which allows you to view the entire raw source of the message. The other, depending on your comfort level with IMAP commands, is called "info" which allows you to send raw IMAP commands to the server (which is essentially the same as using telnet to connect to the server and issue commands).
Hope you find something useful here.