Yes! You can reuse your old Ubuntu Mate 16.04 installation from a Raspberry Pi 3 with a new B+.
Trying to boot the B+ with the old SD without modifications, will result in the rainbow screen with thunderbolt screen showing up.
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From your old Rpi, update the firmware(kernel.img&co) on the boot partition running
sudo rpi-update. This will be enough to boot on the B+ but the wireless card will still not work. -
Set a country code for the wireless adapter in your wpa-supplicant.conf (usually under /etc/wpa-supplicant/) adding
country=GB. -
Get all the files contained in
https://github.com/RPi-Distro/firmware-nonfree/tree/master/brcmand copy them over the content in/lib/firmware/brcm. This will add a few new and updated drivers for the B+ wireless adapter.
If you are performing this step on the new B+, reload the brcmfmac module to enable the wifi:
sudo modprobe -r brcmfmac
sudo modprobe brcmfmac
Once the module is reloaded, the wlan0 interface should appear and the board should connect to the configured wireless AP.
If you are still on the old Rpi3, just switch it off and pop the SD in the new B+, the wifi will not work correctly.