If possible or if you know the direct process of Ethereum network address is accessible on every network with ease. It is only a matter of exporting the private key and importing it to the correct network, please let me know.
You are thinking wrongly here.
You are using an exchange, use the public address that exchange credits to your account and gives it to you. You don't have private key/ mnemonic seed of that public address. Hence you are unable to use its private key to import that wallet on other chains. It is one of risk when you use public address as your receiving address in online account.
both are my account withdrawal and recipient .