It's so much nicer when they are sent as attachments, isn't it?

The classic answer is to right-click the image and use "save as". A common response to that from Mac owners is that they don't know what to do to emulate a right-click, and I can't help you with that.

I have seen a suggestion to view the message as plain text, and all the embedded pictures will then be shown as attachments, but one poster had challenged this. Maybe it works sometimes - it did here with a message which had several embedded images as part of the sender's signature. If this works for you, you can use the "save all" button in the attachments bar to save them.

What happens if you drag-and-drop the image from your message to your pictures folder?

Thanks - should have thought of the "right click" thing myself. I'll try the "drag & drop". Thanks again.