Try this,
var $that = this // here my change
$('input').focus(function () {
var $this = $(this);
$that = $(this);// here my change
$this.closest('p').after($( ".specialCharactersWrap" ));
// alert('test');
});
$('.specialCharactersWrap button').click(function() {
var $this = $(this);
var value = $(this).text();
var input = $that;// here my change
input.val(input.val() + value);
return false;
});