You've just proved my point. You are not pasting the graphic itself but a
link to it.

It's not me, it's Word which decides to paste the link but not graphics.
Outlook's New Message window pastes the graphics Ok.

If you disconnect from the Internet, you will see a red X
instead of your picture.

Ok but so what? The graphics is here, on my PC, just downloaded. It's still
ridiculous (and a shame) that two MS products can't do basic copy-paste
operation between them.

The bottom line is, I can't change it. And that's a pity.