Thank you, Alan. I got the .azw file and examined it. It appears to have no images in it.
The current version of MobiHandler can't show a cover image of a mobi/azw file unless Kindle device shows any on the book's details view (use the RIGHT button on the book on the HOME screen) as in the attached screen shot.
Amazon Kindle for PC (and possibly other Kindle software, e.g., Kindle for MacOS or Kindle for Android) may show cover images even in case Kindle device can't. (See this thread
Also, even if your kindle device shows something appearing as a text-only cover, it may not be a cover image. It can be the first text page of the book.
If anybody has an example mobi/azw file that Kindle device shows a cover for it while MobiHandler doesn't, it should be a bug of my MobiHandler. I love to examine the file. Otherwise, MobiHandler showing no cover image is a behaviour by design, and I can't fix it.