Fijate si te sirve:
Código PHP:
<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<title>Untitled Document</title>
</head>
<body>
<form action="" method="get">
<label>
<input name="checkbox" type="checkbox" id="checkbox" value="a" onclick="if(this.checked)localStorage.setItem(this.id,this.value);else localStorage.removeItem(this.id);">
</label>
<label>
<input name="checkbox2" type="checkbox" id="checkbox2" value="b" onclick="if(this.checked)localStorage.setItem(this.id,this.value);else localStorage.removeItem(this.id);">
</label>
<label>
<input name="checkbox3" type="checkbox" id="checkbox3" value="c" onclick="if(this.checked)localStorage.setItem(this.id,this.value);else localStorage.removeItem(this.id);">
</label>
<label>
<input type="submit" name="button" id="button" value="Submit">
</label>
</form>
<div id="log"></div>
<script type="text/javascript">
document.getElementById('log').innerHTML='Valores checkeados:<br>';
for (var i=0; i<localStorage.length; i++){
var key = localStorage.key(i);
document.getElementById(key).checked=1;
document.getElementById('log').innerHTML+=localStorage.getItem(key);
}
if(!i)document.getElementById('log').innerHTML+='ninguno';
</script>
</body>
</html>