Actually a Russian being hacked by an American will find a very interested FBI - who will promptly send all the needed evidence to whoever in the government deals with overseas issues. In turn this will lead to the Americans proposing an exchange of criminals with the Russians. It might or might not happen depending on details, but the proposal will be made.

Note, the above assumes you are not a target of a US military operation. If the US military is hacking you, then don't waste your time with the FBI (but if that is the case you already have access to "other" means to respond)