Is it possible to use a Bluetooth adapter from one headphone for another?

Question

Bluetooth

There were Platronics ears - they had a Bluetooth adapter specifically for them. I inserted the adapter, pressed the button on my ears - the connection went through. When you connect a USB adapter - the device of the old headphones is displayed in the list of audio devices (not in the Bluetooth list, although they work via Bluetooth), the headphones are dead, I bought others, but they also need a bluetooth adapter, which was not included.
So I think it is possible to somehow file the old adapter on new ears or is it not an option?