Yes, you can:
if (localStorage) { // Browser supports it
localStorage.someKeyName = document.getElementById("MyList").innerHTML;
}
Details in the spec. There are also a large number of tutorials out there.
If you only need it for the duration of a current visit and not between visits, use sessionStorage
instead of localStorage
above.
Note that there are limits on the size of what you can store in web storage, and those limits may vary by browser.
solved Can I save innerHTML of an element to HTML5 Local storage [closed]