So, we have presented the valid reason against the accusation. Please let us know if something is required to clear the doubts. Thank you!
Not enough evidence here. Your identity hide on the domain details. Just one thing matching is both domains had registered from GoDaddy. But fortunately, it doesn't prove anything. Most likely you are right on your claim, but it hasn't backed with enough evidence.
I am not sure if it would be a solution to prove, but you can try it to convince OP that you are the owner of both websites. Just put a noticeable note on both sites and ask the OP to take down this thread. Only he could help you if you may provide reasonable evidence according to OP's expectation.
Thanks for the suggestion, mate. I think redirecting the old domain to new one proves all. What do you think?