Hi Stan,
I just tested this and it looked okay to me.
I changed my photo for my test group (a pretty flower!)
I sent a test message and looked online. Fine.
I sent a test message to my moderator¡¯s subgroup for the travel sight. It maintained the photo I had already in place - actually me, not a flower.
I changed the photo of myself this way:
Online in my group, clicked on my name (top right).
Clicked on Account.
Clicked on Identity.
Use the Edit button to change your picture for the group you wish to change.
Attach your photo and update group.
Frances