<div class="dropdown-menu-portfolio">
  <label>All</label> // This is the text I want to update
  <ul class="category-navbar">
    <li class="select">
      <a>All</a>
    </li>
    <li>
      <a>Item2</a>
    </li>
    <li>
      <a>Item3</a>
    </li>
    <li>
      <a>Item4</a>
    </li>
  </ul>
</div>

$(".category-navbar li a").click(function() {
    $(this)
    .copy(".select a").text()
    .replace(".dropdown-menu-portfolio label").text();
});

$(".category-navbar li a").click(function() {
    $(this)
    .clone(".select a")
    .appendTo(".dropdown-menu-portfolio label");
});

$(".category-navbar li a").click(function() {
    // Modifying the label
    $('div.dropdown-menu-portfolio label').text($(this).text());

    // Removing the class 'select' to the item previously selected
    $('li.select').removeClass('select');

    // Giving the class 'select' to the item currently selected
    $(this).parent().addClass('select');
});

$(".dropdown-menu-portfolio label").text($(this).text());