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I have 2 different third party ones. One from Amazon doesn't work but one from eBay does. 5s here. All worked on 5.

3rd party simply means not made by apple. Doesn't mean they are or are not licensed to work. I'm not an expert though, I could be wrong.
 
I bought this one, so far it is working on my 5s with no error message, and the plastic on the lightning end is nearly as narrow as the Apple one. Should work with most cases.

http://amzn.com/B00ENO0414
 
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