It's not difficult, I think.
HTML Code:
<form action="http://site-b.com/checkout.php" method="POST">
{foreach from=$cart.products item=p}
<input type="hidden" name="products[{$p.productid}]" value="{$p.amount}" />
{/foreach}
<input type="submit" value="Checkout" />
</form>
And at site B you get $products = $_POST['products'];
$products array where ey is product id, and value is amount.
If you have options, it vould be a bit more complicated, but also possible.