I'm going to post this answer under the following assumptions.
1) You (un)selected the checkbox on the first page and submitted the form.
2) Your building the second form and you setting the value="" true/false depending on if the previous one was checked.
3) You want the checkbox to reflect if it was checked or not before.
If this is the case then you can do something like:
var $checkbox1 = $('#checkbox1');
$checkbox1.prop('checked', $checkbox1.val() === 'true');