Apparent tactile motion has been shown to occur across many contiguous part of the body, such as fingers, forearms, and back. A recent study demonstrated the possibility of eliciting the illusion of movement from one hand to the other when interconnected by a tablet. In this paper we explore intermanual apparent tactile motion without any object between them. In a series of psychophysical experiments we determine the control space for generating smooth and consistent motion, using two vibrating handles which we refer to as the Hand-to-Hand vibrotactile device. In a first experiment we investigated the occurrence of the phenomenon (i.e., movement illusion) and the generation of a perceptive model. In a second experiment, based on those results, we investigated the effect of hand postures on the illusion. Finally, in a third experiment we explored two visuo-tactile matching tasks in a multimodal VR setting. Our results can be applied in VR applications with intermanual tactile interactions.