Poser dynamic hair will move with morphs only if grown directly onto the character. This is not a good tactic though as it means that you have modified the figure and when you save the character poser will also save a new obj file. The hair should be grown on a prop, similar to using a skullcap. This prop can be clothified and all added to the constrained group. When a cloth simulation is run it will follow any morphs. This method can be used on things like shoes so that they bend with the foot without going to all the bother of rigging them.