Considering that you have registered customer as admin user and now you have admin username. Esest way to make him autologin will be by creating a file in magento root lets say autologin.php and Now int this file first of all get user
require_once 'app/Mage.php';
umask(0);
$app = Mage::app('default');
Mage::getSingleton('core/session', array('name' => 'adminhtml'));
$username = $_POST['username'];
$user = Mage::getModel('admin/user')->loadByUsername($username);
then initiate secrete key
if (Mage::getSingleton('adminhtml/url')->useSecretKey()) {
Mage::getSingleton('adminhtml/url')->renewSecretUrls();
}
logging in and setting up session
$session = Mage::getSingleton('admin/session');
$session->setIsFirstVisit(true);
$session->setUser($user);
$session->setAcl(Mage::getResourceModel('admin/acl')->loadAcl());
Mage::dispatchEvent('admin_session_user_login_success',array('user'=>$user));
Finally redirect to whatever url you like
//$url = Mage::helper("adminhtml")->getUrl("acompany_mymodule/index/index");
$url = Mage::getUrl('adminhtml/*/*');
$url = str_replace('autologin.php', 'index.php', $url);
header('Location: '.$url);
exit();
So now can create a button anywhere which submits a form to this url BASE_URL/autologin.php with username in post request