Chosen Solution

I need to charge my battery externally. My only concern is overcharging and ruining the battery. I know there is a circuit somewhere that prevents overcharging. Is that circuit built into the battery, or is it part of the phones hardware?

Its in both! The sensors are within the battery and the controlling logic is within the phone. Li-Ion batteries need to be charged with a special charger you can’t just plug any power source to the battery. Here’s a basic writeup on what needs to be done: Charging Lithium-ion. As you can see its a bit of work. Here’s a sample circuit: Make this Li-Ion Battery Charger Circuit. The only problem here is you would need to dig a bit deeper to find out if this would work for a iPhone 4s battery, I’m not sure it would.