I'am in the same case, I need a rear case for my GoPro 3+ black but it is out of stock.
I study the motherboards of the GoPro 3+ black and silver on photos and the unique difference between both it is a contact point between the motherboard and the batterie enclosure. They are not in the same place but there is not a big difference of location (it is lower on the 3+ silver motherboard) . I don't kown to what this contact point use.
There is the same difference in the rear case for the contact point in the batterie enclosure.
It is possible to see that in this photos:
Contact point in the motheborads
GoPro 3+ silver: http://g01.a.alicdn.com/kf/HTB1FS_OIFXXX...
GoPro 3+ black: GoPro Hero3+ Black Motherboard
Contact location in the batterie enclosure
GoPro 3+ silver: GoPro Hero3+ Silver Rear Case
GoPro 3+ black: GoPro Hero3+ Black Rear Case
Everybody know well the gopro and can help us?