So let's hypothetically say we have a 12V 500mAh battery and we want to charge a 4V 2000mAh battery with it, using a (hypothetical) 100% efficiency converter.
One could say that, as the charge is constant in a circuit, one can best case scenario, charge the 4V battery to 25% of its capacity.
However, if one looks at it in energy terms, the first battery could provide, let's say 500mA for one hour @ 12V, this would be converted (with 100% efficiency) to 1500mA @ 4V, so it would (provided the 4V battery could handle the current) charge the 4V battery to 75% of its capacity.
At least one of these two statements is clearly false. I would like to know which one and why. Or if both then what is the real answer.