My father's RR stalled last night, very recently had a warning light and had the battery replaced (Duracell 49(HB)). Was able to get it the last few miles to his home by accessing the battery and hooking up my heavy-duty jump starting pack to start and run the vehicle. Currently have the battery out and on a charger but my question is about these two connectors and which one should be plugged into the sensor on the negative battery clamp:



The one on the left was connected when I removed the battery, the one on the right was tucked down in the battery box. Battery wasn't replaced at the dealership, I have no idea why a shoe print is in the battery box, and I'm just trying to make sure this isn't the issue before I test the alternator. Also, I know there is something like a registration procedure after replacing the battery, I'm borrowing a Foxwell NT680 to handle that but would the battery registration need to be completed before testing anything else? I know on BMW it's a more involved issue and the alternator will overcharge the battery if not registered as well as cause numerous faults, last night I was only seeing a little over 11 volts while the vehicle was running off the jump starter pack which leads me to think the alternator has a serious problem.

 

I don't think the connectors are the same, so only one should plug into the Battery Sensor (Neg Cable). However, the really long lead (should be the one on the right) doesn't go to the sensor. That is there from when the vehicles get shipped on the boat. There is a transit relay on the positive cable that gets removed when the Pre-Delivery Inspection (PDI) is done at the dealer.
The registration process does the same as BMW. The vehicle changes its charging strategy based on its perceived condition of the battery. If the car doesn't know that you replaced the battery (via registration), it won't adjust its charging strategy accordingly and can shorten the life of the new battery.