I wrote on this blog before about the similarity between Husserl's notion of Empathy(Einfühlung) and the simulation theory of mind.
Husserl's theory of the Other (4)
There is another Husserlian term called "sich Hineinphantasieren"(imaginative self-transposal), which is parallel to the notion of simulation. Let me quote the following passage by Natalie Depraz (2001).
Imaginative self-transposal deals with the cooperative encounter of our embodied psychic states, as Spiegelberg named this second stage of empathy after Husserl (Spiegelberg, 1971; 1995).
Again, Husserl has a name for such a second stage. He calls it sich Hineinphantasieren. I am here and I imagine I am going there to the place where you are just now; conversely, you are here (the there where I am going to) and you imagine you are going there, to the place where I am (my here). Literally, we are exchanging places at the same time: through imagined kinaesthetic bodily exchanging we are able to exchange our psychic states. Such a second stage is highly embodied, because it relies upon a concretely dynamical spatializing of imagining.
[Depraz, N. (2001). Husserlian theory of intersubjectivity as alterity. in E. Thompson (Ed.), Between Ourselves: Second-person issues in the study of consciousness, p.173]
You perceive the world, have the variety of feelings and think what to do next, being there (my 'there'). In the same way, I perceive the world, have the feelings and think what to do next, being here (your 'there'). The exchangeability of my here and your here is the ground condition of imaginative self-transposal.
Imagine when you are playing chess with your friend, for example. You will easily understand what Husserl meant by the term "sich Hineinphantasieren". You play chess with partner by virtually exchanging the spatial position and also virtually perceiving, feeling and thinking as your partner does.