TLWN722N_BBB_Ubuntu16.04.2LTS.sh

# Ubuntu 16.04.2 LTS
# rcn-ee.net console Ubuntu Image 2017-07-14
# Beagle bone black

mkdir tmp
cd tmp
git clone https://github.com/lwfinger/rtl8188eu.git
cd rtl8188eu
make all
sudo make install
sudo reboot

# After reboot
sudo ifconfig wlan0 up
# light will be up

if you got

Error! Your kernel headers for kernel 4.4.68-ti-r111 cannot be found.
Please install the linux-headers-4.4.68-ti-r111 package,
or use the --kernelsourcedir option to tell DKMS where it's located

apply

sudo apt-get install git dkms
git clone https://github.com/lwfinger/rtl8188eu.git
sudo dkms add ./rtl8188eu
sudo dkms install 8188eu/1.0
sudo modprobe 8188eu

No need for Debian 9.5 / BBB img.