Jquery function doesn't work after Ajax call

That is because you are using dynamic content.

You need to change your click call to a delegated method like on

$('.post_button, .btn_favorite').on('click', function() {

or

$("body").on( "click", ".post_button, .btn_favorite", function( event ) {

Instead of this:

$('.post_button, .btn_favorite').click(function() {

do this:

$(document).on('click','.post_button, .btn_favorite', function() {

on will work with present elements and future ones that match the selector.

Cheers