Ubuntu 16.04, Acer laptop, Broadcom driver and wifi cannot be enabled

Ingredients

• Laptop Acer Aspire V11 Touch
• Ubuntu 16.04 (kernel 4.4.0-45)
• Additional driver ‘Broadcom 802.11 Linux STA wireless device’ in use

• lspci -knn | grep Net -A2

  02:00.0 Network controller [0280]: Broadcom Limited BCM43142 802.11b/g/n [14e4:4365] (rev 01)
  Subsystem: Foxconn International, Inc. BCM43142 802.11b/g/n [105b:e07e]
  Kernel modules: bcma, wl

• rfkill list

  0: acer-wireless: Wireless LAN
  Soft blocked: no
  Hard blocked: no
  1: acer-bluetooth: Bluetooth
  Soft blocked: no
  Hard blocked: no
  2: hci0: Bluetooth
  Soft blocked: no
  Hard blocked: no

Issue

I cannot see any option to enable the wireless device from the applet main menu bar. As a result I cannot activate and use the wi-fi.

Research

I am almost-fully aware of this extensive post on Installing Broadcom Wireless Drivers, but installation is not the point. However, I have followed the uninstall/install sequence:

sudo apt-get purge bcmwl-kernel-source
sudo apt update
sudo update pciids
sudo apt install firmware-b43-install
sudo reboot
sudo apt install bcmwl-kernel-source # corresponds to my PCI id 14e4:4365 (rev 01)
sudo rfkill unblock all # for good measure

to no avail. Note that at sudo apt install bcmwl-kernel-source a dialogue window asks permission to disable Secure Boot by typing an ad hoc password. It claims it will be asked later, although I did not see it being asked again.

Interestingly, from this bounty-winning answer https://askubuntu.com/a/199154/446253, I could see with lspci -nn | grep -i BCM that my network controller is a BCM43142 that might not be supported by the STA driver. This is way too esoteric for me, but it may provide a clue to the expert.

I am also aware of other posts that deal with earlier Ubuntu versions, but I would dearly avoid guesswork and find an answer that applies to 16.04 safely.

Question

Please could you provide a list of simple steps to regain the possibility to enable the wifi from the menu bar?

If you need to refer to verbose posts, please indicate which answer is applicable according to you and in which way it integrates the actions undertaken above.