You have to extend 'icon_system_fontawesome.php' in your theme as a new class, then override the method 'get_core_icon_map', call the parent and then alter the returned 'map' to have your value for the icon, then return that changed '$map', then in the theme 'config.php', tell Moodle about your class, i.e. "$THEME->iconsystem = '\\theme_mytheme\\output\\icon_system_fontawesome';". If you want to see a slightly more complicated implementation that works along the same lines, then look at my Foundation theme.
Themes
changing the font awesome icon of the 'send message'
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