Have you had a decision from the tribunal yet?
It seems that the judge has made a factual finding that the claimant did report a change. Presumably this was based on oral evidence from the appellant. Unless that finding was so unreasonable that no other tribunal could have made it you can’t really do much about it.
I would normally look into the claim history and bring this to the tribunal’s attention. Did the claimant always report changes by writing a letter? If she usually came to the Council in person or reported changes by telephone you would have had the chance to query why she changed her preferred method of communication. Does she say she sent original documents? If so she presumably expected them back at some point; why didn’t she query this?