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I did that and copied the URL into a Word document.  The link does not work, but when you copy and paste the link into the search engine it does bring up your Voki character.  You can also e-mail the character to yourself.  That seems like a programming error on the part of Voki so I would notify them.

When you hit the link button it says copy URL and the  URL is to the right.  

When you create your Avatar next to the Avatar it says share Voki Character.  Then it has various places where you can share the Avatar and it also shows a link button.  I think you would click on the link button and follow the directions from there.  If that's what you are doing and it is not working, I don't know.  Can you put in a help ticket with Voki?