Well I guess you can store Y on the session for id:2 to pick it up, but seems inelegant. Maybe perhaps a parent conversation, spawning a child conversation for your wizard. The wizard does it's magic (pun intended) and posts the Y conversation to the parent and then another child conversation is created and takes Y from the parent and does what you need.
But now after typing all of this. I think you will have a more fulfilling solution if you just keep Y at the parent conversation, and have id:2 and id:1 manipulate it, since you cannot change the mapping of Y, you can change it's properties and invoke it's behaviors.