The quickest way to do it may be to use the NLA clips feature. Pose your figure, makes sure your figure is selected and click the NLA tab and select Master Pose. You will be asked to name the pose and it will then be available under the clip tab. Drag the clip to the figure you wish to pose, make sure it is at the beginning of the time line, and viola! Duplicate pose.
You can save your pose to the Browser, by dragging the clip icon from the clips tab and dropping it on the Clips section of your browser. It might help to set up folders for such clips based on models with the same rigging, such as a folder for M3 and a different folder for M4, etc.
I should add that I don’t know if it saves morphs or not, so you may want to play around with it to test it.