I believe I've found a solution to my problem. Not sure if it's a problem with Chrome, Evernote, or if I'm just doing it wrong.
Working with desktop PC and Evernote web client. I want to copy an image from Chrome (e.g. Facebook web) to a note.
I right-click the image and I choose "Copy image". Then I paste the image to Evernote web.
I expect the CONTENT of the image to be copied. Instead, only a LINK to the image is added to the note. This can be verified by exporting the note from the desktop app to a file and checking its contents. Later on,