There's basically no way to fit a battery with more than 3000 mAh into the G4 and still use the original back. I'd recommend getting another OEM battery and swapping when the first gets low. If you'd prefer an extended battery, which is heavier and requires a bigger back door, I'd go with the Mugen 6200 mAh or the Hyperion 6000 mAh. I'm sure the ZeroLemon lasts forever, but that will turn your phone into a brick.