Battery connector broke when doing repair

I was attempting to replace my battery for these headphones, and the one I used instead had a different connector that just looked very visually similar, and when I put it into the battery connector it did not work, and in attempting to remove it, I snapped off the battery attachment accidentally. I assume I will need to resolder the battery connector if I am to have any hope, but am wondering if people know how it connects to the circuit board, and the best way to resolder it.

If this is impossible, is there a way to replace the whole circuit board, or would it be better to just replace the headphones entirely? I am open to going to an outside person as my experience with soldering is still somewhat limited.