Will Apple repair my AirPods?

My AirPods Pro are experiencing an issue at present where the left AirPod is not responding at all. The battery indicator shows it is at 100% charge, but this does not change, and the AirPod acts as if it is broken. I think it may be dead.

I lost the charging case for my AirPods a few months ago, and my friend had lost the AirPods from his - so he gave it to me, and I had been using it to charge mine.

If I send this off to Apple for repair, will they fix it as the serial numbers will not match? What should I do?

Thank you in advance.