Use a delegated event handler bound to the container:
$('#pg_menu_content').on('click', '#btn_a', function(){
console.log(this.value);
});
That is, bind to an element that exists at the moment that the JS runs (I’m assuming #pg_menu_content exists when the page loads), and supply a selector in the second parameter to .on(). When a click occurs on #pg_menu_content element jQuery checks whether it applied to a child of that element which matches the #btn_a selector.
Either that or bind a standard (non-delegated) click handler after creating the button.
Either way, within the click handler this will refer to the button in question, so this.value will give you its value.