seems like they own that wallet with 1000+ ethereum based on my personal research.
Your research is based on the ~1300 ETH address sending some amount to the 10 ETH address.
This is not a good way of establishing proof of ownership since I can do the same thing by withdrawing Ethereum from an exchange. The exchange's input address would most likely have a huge amount of Ethereum, right?
Simplest way is to sign a message.
That make sense though would someone normally transfer his ethereum from one exchange to another? As you can see the incoming balance are all from binance. Would you also mind telling me where would a sign appear? Is it on the comments or input in etherscan? Thanks