Transfer charge from a battery to another battery storage
Make a buck-boost converter that draws power from the one battery. Then make a charge circuit that can charge the other battery. Spec it so that the input of one is the same as the output of the other. Combine the two and you can transfer charge from one to the other. 

You could probably make a buck-boost converter with an efficiency around 97 percent. You will also have loss in the charging circuit i'm not sure how efficient this could be. 

This will in reality be a battery bank, that instead of charging your phones battery, charges another battery. 

With the popper protection and isolation it will also be possible to connect them in parallel or in series. This is effectively what is done in multi-cell LiPo battery packs.