Sent ETH on the Arbitrum network

Hello everyone. I recently tried cashing in some crypto to a betting website, I decided on Etherium and used the Arbitrum network since the fees were so low. However, after a few hours of waiting the funds were still not in the website, so I contacted support. They told me I shouldn’t have used the Arbitrum network since it’s not supported and they don’t know if they will be able to do something about my situation. However, I also read that the funds can be recovered if they just create a wallet on the arbitrum network using the private key from the original address. Is this true and does anyone have experience with this? Thanks in advance…