localstorage.js

<script>
  // test for localStorage support
  if(('localStorage' in window) && window['localStorage'] !== null){

  var f = document.getElementById('mainform');
  // test with PHP if the form was sent (the submit button has the name "sent")
  <?php if(isset($_POST['sent'])){?>

    // get the HTML of the form and cache it in the property "state"
      localStorage.setItem('state',f.innerHTML);
 
  // if the form hasn't been sent...
  <?php }else{ ?>

    // check if a state property exists and write back the HTML cache
    if('state' in localStorage){
      f.innerHTML = localStorage.getItem('state');  
    }

  <?php } ?>

  }
</script>

I´ve removed an extra ")" from php if :)