Ask HN: How to clone a wi-fi network completely?

I have a wi-fi client in our heat pump, that is hard to access for reconfiguration. I want to change my network setup, and before doing that, I would like to move that client to a new device.

I've setup a new router (running dd-wrt), using same SSID, mac cloning (same BSSID), same subnet mask, same channel, same security method... but the client is not able to connect to the new device yet.

What else is there to clone? Could it be a difference in the chip on the router? What are good ways to migrate such wi-fi clients to a new device?