You should resist this. If the customer can't provide credible evidence that you are at fault then you really have nothing to say to him. I would imagine that even the other company would have difficulty in saying categorically that you were at fault when you did your work in March and the fault was in June. I don't know the tech details of course. However, by refusing to give you any information, the customer is acting quite suspiciously. And you are quite right. He can't ask you to refund him and also pay for the second company. This all just sounds like nonsense to me and I would be telling the customer where to put his allegations. Confirm in writing to him that he has failed to give you fair notice of the issue, has had further work done, has not shared any information and all of those failure will be founded on in the event that he is unwise enough to take this further. He can't litigate by ambush. He has to give fair notice. He hasn't done so. Happy to discuss further. I hope that helps. Please leave a positive rating so that I am credited for my time.