2032 Battery you need - https://amzn.to/2MsYPrd

Suitable for the following vehicles

MINI Cooper All Models 2015 2016 2017 2018
MINI Cooper Clubman 2015 2016 2017 2018
Genuine Part No.:9367411-01, 185409-10

FCC ID:NBGIDGNG1

Model:IDGNG1
434Mhz Hitag3 Chip

OEM Smart Remote Key Fob 4B 434MHz for BMW Mini Copper 2015-2018 Fcc # NBGIDGNG1

How to Program the Key for a Mini Cooper
Insert your key in the ignition of your Mini Cooper. Turn the key until the interior dashboard lights turn on.
Remove the key from the ignition, but do not turn the key to the "off" position. Push the "Unlock" button on your car-key remote. ...
Push the "Lock" button three times.

To test the new battery, stand near your MINI and press the "Unlock" or "Lock" buttons.
If the new battery is working properly, you should see the parking lights flash and also hear the door locks opening or closing.

The fob shouldn't need to be reprogrammed. Just changing the battery shouldn't clear the original programming.