doesn't save a value

There are some drawbacks to this solution. See issue #2370899.
Basicly what my module does is hide the original select element and change it (invisibly) when an icon is clicked.
You can show the select again by making it visible in webinspector, or by modifying my CSS. If you make it visible, you should be able to see it change if you click an icon.
It sounds to me like a javascript error is causing this not to work. Do you see an error in the javascript console?

I can verify that I am getting the same error too. The console error I am getting is

Uncaught Error: Syntax error, unrecognized expression: [data-select-name='quick_fact_icons_iconmoon|icons-qf-megaphone'

Could this have something to do with the Jquery Update module? We are currently using JQuery 10 and the Adminimal theme. If you need me to volunteer more information let me know.

Otherwise, great module!

Might very well be that a newer version of jQuery causes some issues. I'll test and get back to you!

I have just released a new version and tested it in jQuery 1.10 as well. Should work now.