After I run wordpress_update_publish, it does not update the groups:

$update = array('ID' => 1623, 'post_category' => array(219), 'post_content' => "Test");

wp_update_post($update);

I ought to point out that it will update the publish using the publish_content, therefore the publish has been up-to-date, however i have no clue why it isn't upgrading the groups.

Any assistance is appreciated. Thanks!

Whether it's a custom taxonomy use:

wp_set_post_terms() 

to create the course for any publish. Then use:

wp_update_post();

to update the publish the category was set to.