Drupal 7 - Retain checkbox values across pages
Store the selected checked box in a database. Load each check box as the pagination goes and check the #default_value

example if I had 3 checkbox in a table select for my pagination:

$values = array();

$values[1] = TRUE;
$values[2] = FALSE;
$values[3] = TRUE;

$form['table'] = array(
    '#type' =&gt; 'tableselect',
    '#header' =&gt; $header,
    '#options' =&gt; $options,
    '#default_value' =&gt; $values,
    '#empty' =&gt; t('No campground to claim'),
  );


Obviously there is more to this, like pagination, but it should get you on the right track.