Drupal 7 | How to pass a function callback via drupal_add_js to module js?

Question

Setup: Module has its javascript file with the following functions:

(function ($, Drupal, undefined) {
    Drupal.behaviors.mymodule = {
        attach: function (context, settings) {
            var userSettings = settings.mymodule;
            var myFunction = userSettings.passedFunctionCallback;

            function a() {
                return 'a';
            }

            function b(){
                return 'b';
            }
        }
    }
})(jQuery, Drupal);

If I wanted to assign variable myFunction a function i would simply do this in javascript:

myFunction = a;

Problem comes when I want to pass this callback via Drupals drupal_add_js:

drupal_add_js(drupal_get_path('module', 'mymodule') . '/js/module.js');
drupal_add_js(array('mymodule' => array('passedFunctionCallback' => 'a')), array('type' => 'setting'));

In my js, passedFunctionCallback is a string and not a function callback:

myFunction = 'a';

Question is: How to pass the variable as function callback via drupal_add_js (if its possible)? Are there any workarounds?