If you build and sign a valid transaction transferring 1 Eth from your account A to another account B, this is exactly what the transaction will do, whoever submits it, and to whatever RPC it's being submitted.
If an external actor was attempting to take your transaction, replace the receiving address by an address of their own, then the transaction signature would not be valid anymore, and would be rejected by any node on the network.
To elaborate on your example, submitting a transaction to an RPC doesn't involve a wallet at all, it's just sending an RPC request containing the signed transaction. So the statement "wallet B sending a transaction signed by wallet A" does not make sense here.
Are you hoping to use the signature, or what?
Are you hoping to execute the transaction on another account… which is not what you Asked?
Are you hoping to execute a different transaction on another account?
– Robbie Goodwin Aug 26 '23 at 21:53It might be vitally important and whatever you meant, 'I'm trying to replicate the example I gave, execute transactions which have been signed. The accepted reply answers this is possible. I didn't realize it didn't have to be sent by an EOA, rather just the signed tx has to be sent through an RPC…' simply does not work in English
– Robbie Goodwin Aug 27 '23 at 18:00I'm sorry you don't mind that jj1980's Answer lacks too much in English to be worth the screen it's Posted on, and that remains youir choice.
– Robbie Goodwin Aug 27 '23 at 22:16