Electrons move inside the battery as well. Battery also has a cathode and anode. So, electrons move inside the battery as well and through the entire circuit.
From the negative terminal of battery, electrons move through the circuit and comes to the positive terminal of battery. Then chemical reactions occur inside the battery and these electrons move again to the negative terminal. But this movement is in the form of movement of ions inside batteries.

Write your answer.. toh sir conductor ke electrons move nahi karenge kya?