Magento 1.9 moving products between websites

Question

How to move a product/item who was added to cart/quote on websiteA to cart/quote which is on websiteB.

I would like to solve this problem with controller, but I am not very successfull.

Do you suggest something different?

code in my controller:

$oldQuote = $session->getQuote();
$oldQuoteItems = $oldQuote->getAllItems();
$newQuote = Mage::getModel("sales/quote")->setStoreId(1);
foreach ($oldQuoteItems as $_item) {

    if ($helper->checkProduct($_item->getProduct())) {
        $newQuote->addItem($_item);
        //$oldQuote->removeItem($_item);
    }
}


try {
    $newQuote->collectTotals()->save();
    $oldQuote->collectTotals()->save();
}

Thanks for the help