You are eligible to use the Costco warranty without the receipt. They do not need it to replace a faulty battery that is within the warranty period. This is why you must have a Costco membership to buy from them. All they need do is go to their system since all your information is already there.  However, for Costco to do battery replacements without a receipt, the original purchaser will need to provide the old battery. They will use the battery's serial number to track the purchase that was made. But, if you provide your receipt, the process will be faster since they will get all information from your receipt at a go.