Here is a fix that works, from a comment on the plugin's page (https://moodle.org/plugins/block_quickmail?nonjscomment=1&comment_itemid=52&comment_context=50&comment_component=local_plugins&comment_area=plugin_general&comment_page=0)
Simply Modify /blocks/quickmail/js/selection.js at line 53
Change: return $("#mform1").submit(function() {
To: return $(".mform").submit(function() {
After you are done simply save and clear the server cache...then it works!