Why my iPhone 4 is not charging?

I repair phones quite often, and a client brought me an iphone 4 on which he has damaged the battery connector. A friend of him tried to repair it, but removed the 4th small component in the red square on the picture beside this text. (a 240-OHM-0.2A-0.8-OHM inductor)

Since, then, when the phone is plugged, it indicated that it is plugged, but the battery doesn't charge, as shown on the second picture.

I put a wire between the pin n#2 of the battery connector and the 3rd component, but it is still the same.

The phone simply acts as if the second pin of the battery was not connected at all.

I tested the fuse but they are fine. I even shunted the USB power IC but the result is still the same. (these components are presented on picture 3).

I made an experiment. I removed the 240-OHM-0.2A-0.8-OHM inductor on another working iphone. I put a wire from the 2nd pin of the battery to the 2nd solder point of the inductor (starting from the left), and the result is the same : iphone not charging. It means that the first solder point is essential to make it work. The problem is : this solder point was removed by the guy who made this bad work before and removed this component. So the question is : where should I connect the second pin of the battery connector to make the phone charging, knowing that I cannot connect it to the solder point of the inductor ?

Picture 4 is presenting the removed component on the working phone. We can see that the two solder points are in perfect conditions, and I managed to put back the component after.

I finally managed to take some acceptable pictures of the damaged area on the phone. On picture 5 is the damaged area after cleaning.

As jessabethany suggested, I tried to scratch the area, but the only piece of copper I found seems to be a bit low, as shown on picture 6

I made a solder between this tiny piece of copper and the other point, but the phone is still not charging. To be clear with this last picture, the wire goes to the second pin of the battery, and the blue tape is to avoid any contact with the ground of the battery.