Shift+Alt+Down does not work as Shortcut for PHPStorm or any other app Ubuntu 18.04

Try a basic keyboard configuration. In my 16.04 and 18.04 it is setup like this:

$ cat /etc/default/keyboard
# KEYBOARD CONFIGURATION FILE

# Consult the keyboard(5) manual page.

XKBMODEL="pc105"
XKBLAYOUT="us"
XKBVARIANT=""
XKBOPTIONS=""

BACKSPACE="guess"

There is a bug report: Unable to use shortcuts with keyboard layout switcher on Ubuntu MATE, 16.04 (with HWE), 17.10 and 18.04 LTS

Unfortunately the bug report has no fix yet.

Fortunately there is a solution that might work posted by Norbert in another forum: Keyboard layout switching problems and poll:

sudo add-apt-repository ppa:nrbrtx/xorg-hotkeys
sudo apt-get update
sudo apt-get dist-upgrade

Please read both links thoroughly before proceeding.