Thanks. That was really useful. Even though it didn't fix that particular smilie, it did fix all the others. The one I was watching didn't change. That broken image link is still there. The others were previously coming through as text and they have all changed to smilies now.
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Any idea what the problem could be with the first one? In the message it displays as the same standard smilie that's used at the bottom of this screenshot. It's strange that it displays correctly in the message but not here.