I don’t know what the first part of your comment is trying to say. I agree that counterfactual mugging isn’t a thing that happens. That’s why it’s called a thought experiment.
I’m not quite sure what the last paragraph is trying to say either. It sounds somewhat similar to an counter-argument I came up with (which I think is pretty decisive), but I can’t be certain what you actually meant. In any case, there is the obvious counter-counter-argument that in the counterfactual mugging, the agent in the heads branch and the tails branch are not quite identical either, one has seen the coin land on heads and the other has seen the coin land on tails.
Am I correct in assuming you don’t think one should give the money in the counterfactual mugging?