but I can tell you what I usually do.
Forwarding emails is often, 'patchy'. Some users have their email software set to enable HTML, others do not, and that can cause email forwarding problems. Other users have image display disabled, and whether that means the image is never downloaded from the server in the first place, I can't say. Also as you have tested, emails in HTML with links to web site images can fail if those images are removed from the web site or web page.
Your testing was spot on. You grabbed the url, (the http address), opened your browser, and pasted the url into the address bar to see the images from the web sites themselves. But if they were not there, then the problem is not with you, but elsewhere.
So, I gave up on forwarding complex emails a while ago. If I want to do that now, I save the images to my Desktop, (temporarily), then create a new email and either insert them into the body of the email, or attach them to the email.
That seems to work for me nowadays.
I use Thunderbird for email.
A friend FORWARDED me (using Yahoo email facility) an email containing a series of some pictures, and those pictures appeared right away in the body of the email on my screen (that is, I did not have to click on any attached jpg icons to view the pictures one by one. There were no attached jpg icons anyway.)
Before forwarding the same email with the pictures to a friend of mine, I forwarded it to myself to test whether the pictures would arrive in my Inbox faithfully. They did not. In the place of the pictures, wording something akin to a corresponding http address appeared in my Inbox (as well as in my Sent box). I copied those http addresses in my Firefox browser to see if those pictures can be seen at least one by one on the screen. I could not. Some error message appeared each time.
Incidentally, I had forwarded the above email to myself using, one by one, EACH of the three available options: (1) Send in Plain Text and HTML; (2) Send in Plain Text only; and (3) Send in HTML only. None of the three options made any difference.
What is the source of my inability to FORWARD pictures (which had in fact been FORWARDED to me by my friend), and what is the solution to the problem?
Thank you very much.