I think I have a solution. You have both the bcm43xx....deb file and the wl_apsta-22.214.171.124.o file. Correct?
Put the .deb file somewhere convenient, right-click on it and choose 'Extract here'. You'll get a folder extracted containing the contents - control.tar.gz and data.tar.gz. Do an 'extract here' on data.tar.gz and you'll get a /usr folder containing /bin and /share folders. In the /share folder is yet another subfolder called /bcm43xx-fwcutter, and in that folder is the executable script install_bcm43xx_firmware.sh. The script in the version I downloaded consists of this:
But check yours. There were a few versions of the bcm cutter package to choose from. In the /bin folder is the executable bcm43xx-fwcutter. So, as far as I can see, all you have to do is put the bcm43xx-fwcutter executable and wl_apsta-126.96.36.199.o file in the same place, and do each command in the script from the 'bcm43xx-fwcutter $dname' line, adapting that to:
if [ -e /usr/bin/wget ]; then DL="wget -O $dname"; fi
if [ -e /usr/bin/curl ]; then DL="curl -o $dname"; fi
mkdir -p /lib/firmware
for i in *.fw; do
mv $i /lib/firmware/$i;
The for - done loop you could probably do as a 'sudo mv *.fw /lib/firmware/'.
sudo ./bcm43xx-fwcutter wl_apsta-188.8.131.52.o
As far as I can make out bcm43xx-fwcutter must extract a number of *.fw firmware files from wl_apsta-184.108.40.206.o, which you need to move to lib/firmware. And that's it really.