Install the following packages.
sudo apt install language-pack-ja fcitx-bin fcitx-mozc
Log out, then log back in.
There should be a keyboard icon in the bottom right. Right click that icon and 'Configure.'
Click the plus icon. Make sure to uncheck 'Only Show Current Language.' Search for mozc, select and click OK.
You can toggle between input methods using Ctrl+Space.
ドじゃああん!