When you sign for acceptance of unchecked goods you should sign, "goods not inspected at point of delivery," however that will only give you a short opportunity in which to reasonably notify them that the goods were actually damaged upon arrival, especially as you plan to remove the goods to a different address to which they were originally delivered.
This reasonable period will only be a couple of weeks after the delivery date, therefore to cover yourserlf you should remove the packaging and thoroughly inspect the goods at the point of delivery. Then and only then when you are happy... should you sign as received in good condition, afterwards replace the packaging as securely as you possibly can.