Broadcom BCM4356 driver

Your device is covered by the driver brcmfmac in Ubuntu 15.10. It also requires firmware that is included in linux-firmware-1.149 and later. Let's install the latest firmware first. Download this package to any convenient place. https://launchpad.net/ubuntu/+source/linux-firmware/1.156/+build/9020816/+files/linux-firmware_1.156_all.deb Right-click it and select 'Open with Ubuntu Software Center' and install it.

Now open a terminal and do:

sudo apt-get purge bcmwl-kernel-source
sudo modprobe -r brcmfmac

The last command may end in an error; that's fine, just continue:

sudo modprobe brcmfmac

The wireless should now be working.

I'm running a Lenovo T560 with Broadcom 4356 on Kubuntu 18.04.1 LTS and using linux-firmware_1.156, wireless works. But, when updating packages, all newer linux-firmware in use, disconnected me from wireless.

So I just followed the steps mentioned above and afterwards, I put the package on hold:

sudo apt-mark hold linux-firmware

Thus, the package stays at the same version (1.156).

At some point there may be linux-firmware, that supports Broadcom 4356 again, then simply replace "hold", with "unhold" in that CLI command and then run the update.