<?php
if (!$_POST['sheet']) {
    $processor = 'sheet/create';
} else {
    $_POST['id'] = $_POST['sheet'];
    $modx->setPlaceholder('id', $_POST['id']);
    if ($_POST['remove']) {
        $processor = 'sheet/remove';
    } else {
        $processor = 'sheet/update';
    }
}
$processorProps = array('processors_path' => $modx->getOption('core_path')
                . 'components/exam/processors/');
$response = $modx->runProcessor($processor, $_POST, $processorProps);
if ($response->isError()) {
    $hook->addError('process_error', $response->getMessage());
    return false;
}
return true;

<?php
class ExamSheetUpdateProcessor extends modObjectUpdateProcessor {

    public $classKey = 'ExamSheet';
    public $objectType = 'object';
    
    public function beforeSet() {
        if (!$this->modx->user->id) return 'Вам нужно авторизоваться';
        if ($this->object->get('created_by') != $this->modx->user->id)
            return 'Вы не можете редактировать чужие записи';
        return true;
    }

}

return 'ExamSheetUpdateProcessor';