@Cyraxote 

You might be able to save a lot of network headache not just for the TP-Link/Kasa products but for other devices as well if you use the same network names and passwords as you are currently using.  A majority of devices should just connect but some may still need to be reset and reconfigured.  

  @Carl 

That's an interesting idea. Do I lose anything by doing that, I wonder...?

  @Cyraxote 

No you shouldn't at all.  Some devices might be bound to the MAC of the existing router in which case even if the same SSID and Password are used they will need to be reset and reconfigured but most newer device will simply look for the SSID and if they see the one they are configured for they will attempt to authenticate.  As long as the password is the same they should connect and give you the seamless transistion.