When battery is not connected, the outer surfaces will have charge +q and inner faces of the plates will have zero charge each.

When a battery is connected to the plates of the capacitor the charges on the plate redistribute in such a way that the potential difference between the plates becomes equal to the emf of the battery.

So, the inner surfaces will have equal and opposite charges according to Q=CV

Where C is the capacitance and V is the emf of the battery. Thus we can say that the battery supplies equal and opposite charges CV) to two plates.

And the charges on the outer surfaces remain same as on connecting the battery only charges are transferred and total charge remains constant so to have zero field inside plate the outer face charges have to be same.

Therefore when a parallel plate capacitor with each plate having charge q is connected to a battery then the facing surfaces have equal and opposite charge and the outer surface will have equal charge.