The BMW item is identical and costs just a few pounds more. Used across a wide range of BMW bikes, it is commonly stocked accessory.
Edit. If that photo is of your bike, you have the BMW accessory lead plugged in already. Follow the route of the wires that extend from the white plug and nip them off at the other end.
Before you cut any wires, wait for about ten minutes after the ignition key is removed, as the bike continues to power the accessory port for a few minutes following ignition shut down.