As default user run the following commands:
id # shows the groups you are a member of
id <otheruser> # shows the groups the other user is member of
sudo usermod -a -G <groupname> <username>
The last command makes the username part of the groupname by adding the groupname to his account settings. Don't forget to use the -a option in that command as without it all existing groups he was member off will be wiped. (the -a stands for add)
Warning: adding the sudo group to this account will give him full power over the computer. You should test if adding another groupmembership will be enough for shutdown/reboot. Can't advice you there.
Medion S4216 Ultrabook, 4GB RAM, 1TB HDD, WIN 10 & Bodhi 4.1.0-64
Asus eeepc 901, 1GB RAM, 12 GB SSD, Bodhi 3.0.0-32-Legacy & Bodhi 4.1.0-32 Legacy