Left shift key doesn't work - how to map it or fix it? or it's never worked?

That looks like an English (international) layout, which features the two-row return key.

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Keyboard Viewer (built into MacOS) will darken any key on the keyboard (replica on the screen) when the actual physical key is depressed.

System preferences > Keyboard > Keyboard > [√] show keyboard ... viewers in the menu Bar

Then from the MenuBar, click on the Icon for those Viewers and choose Keyboard Viewer. A tiny keyboard replica appears on the screen. Press any key on the actual Physical keyboard to see if it indicates it is being depressed by darkening the key in keyboard Viewer.

For remapping:

http://matthewpalmer.net/blog/2014/01/19/remap-keyboard-keys-caps-lock-os-x-mave ricks/

https://pqrs.org/osx/karabiner/

Open the Keboard View and sii what that show when you depress the left shift key:

http://www.imore.com/how-use-keyboard-viewer-your-mac

This will show you what the OS thinks is depressed. If it shows nothing then likely bad key

You should know if it has never been working. Or is this a second hand machine. If so, there may have been a liquid spillage by the previous owner.

Perhaps it was sold because the previous owner knew about it. Where did you buy it from?

You figured what?