Сохраните текст Div в LocalStorage, обновите LocalStorage при изменении текста
// get the text
var text = $('#test').text();
// set the item in localStorage
localStorage.setItem('test', text);
// bind text to 'blur' event for div
$('#test').on('blur', function() {
// check the new text
var newText = $(this).text();
// overwrite the old text
localStorage.setItem('test', newText);
// test if it works
alert(localStorage.getItem('test'));
});
Excited Elk