Toothbrush works but does not charge

Hello, I have two sonicare toothbrushes and both of them work fine but do not charge. I am trying to pin down the reason. I opened them both and the connectors from the induction coil to the PCB seem OK. The battery seems OK as well (it is powering the toothbrush and the voltage reading is correct).

Any idea how I can troubleshoot this? One thing I thought about is to measure the voltage coming from the induction coil into the PCB, but I don’t know how to do that. Do I need a multimeter with a small AC voltage tolerance (the one I has settings for 100V and 200V)? Any other ideas?

Thank you.