Created attachment 579754 [details]
Outlook view example

Created attachment 579758 [details]
evolution replying

When I reply problem message, in composer window pictures are displayed.

Thanks for a bug report. Current git master (to be 3.5.1) doesn't suffer of this, but I can reproduce it with 3.4.1. The image is properly shown if you scroll at the very bottom, where is shown "PNG image attachment", which if I let show inline (by clicking the left side of the button), then it's shown in its original position too. I have other message with inline image which works properly.

The difference between yours and mine message is that yours is defined as
   multipart/mixed
      text/html
      image/png

while that mine is defined as
   mutlipart/related
      mutlipart/alternative
         text/plain
         text/html
      image/png

The difference between multipart/related and multipart/mixed seems to cause the issue here.

I fixed this for 3.4.2+ of evolution.

Created commit c40339c in evo gnome-3-4 (3.4.2+)