There is an adapter kit required to mount the 2013+ battery in the 2011/12 model. Based on that, I would say the 2012 battery will not bolt up to a 2013. Swapping battery packs requires dealer support to program the car to recognize the BMS in the battery pack. Taking the cells out of a 2013 case and transferring them to a 2012 case (using the original BMS) gets around that problem, and gives an older model new life, but is quite a project. From what I have read, the 2012 case is resealable, but the 2013+ is not.
2013 Leaf SV - Cayenne Red - QC Port - LED Headlights