Many excellent architectures exist that allow imitation of actions involving observable goals. In this paper, we develop a Simulation Theory-based architecture that uses continuous visual perspective taking to maintain a persistent model of the demonstrator's knowledge of object locations in dynamic environments; this allows an observer robot to attribute potential actions in the presence of goal occlusions, and predict the unfolding of actions through prediction of visual feedback to the demonstrator. The architecture is tested in robotic experiments, and results show that the approach also allows an observer robot to solve Theory-of-Mind tasks from the 'False Belief' paradigm.