Send them the link to the transaction:
https://blockchain.info/tx/f1f6a0d8a24a6fac35fa6b4f673e5ce3d820c400db73f798b15aa0b9abf52268Along with a screenshot of your wallet with the transaction showing... Then ask them to supply the goods or services you have paid for.
The transaction has over 1760 confirmations and has been confirmed since 6th September.
They're either trying to scam you or they don't know how their wallet works and/or how to fix it. They say you should never attribute to malice that which can be explained by incompetence... But something seems fishy here.