Where to exchange data between two states in the code so not to introduce a global variable and without a Singleton?

Suppose an FSM has two states:

1. S1 generates some data
2. S2 needs exactly that data

So the precondition of S2 is the postcondition of S1.
This psudo-code comes to my mind:

// method: changeState()...        
switch(changeTo){
    case "S2":
        // done with existence verification...
        S2 = stateFactory.byData(S1.getData());
        FSM.changeState(S2);
        break;
}

This will introduce additional argument for the factory and could make long switch with data processing too, where the switch is to be just a switch.

When it comes to code design, where is the best place / how best to do this data exchange?