Raise it from the order, with the store. Not with the courier.
That sounds like being passed along and it is the opposite: it is the route where somebody owes you something.
Why not the courier
You have no contract with them. The store booked the delivery, so the courier's customer is the store. A courier talking to you is doing you a favour and is not obliged to.
You do not have the booking reference. The store does.
Their claim process is for the sender. Even when a courier pays out, it pays the person who booked it.
So going direct means asking a company that owes you nothing to help you with a reference you do not have.
What happens when you raise it properly
The item is damaged, so it is covered. Damaged, faulty, wrong or not as described can come back for 7 days whatever the store's own policy says. The courier's role does not change that.
It is the store's job to sort out, including whatever they can recover from the courier. That is between them.
Metzee decides if you disagree, within 48 hours of a dispute being opened. How refunds work
What to send, in the first message
This is the part that decides how fast it goes:
Photographs of the box before you unpack further. The outer packaging is the evidence, and people throw it away first.
Photographs of the damage, in daylight, with something for scale.
The label, showing it is the right parcel.
An unboxing video if you have one. Not required, and it ends the conversation when it exists.
What not to do
Do not throw the packaging away. The single commonest mistake. A crushed box photographed is worth more than any description of it.
Do not repair it first, however easy it looks.
Do not go to your bank. Slower, and it takes money back out of a small store weeks later. What is a chargeback?
If the store blames the courier
They may be right about the cause and it changes nothing about the outcome. The item you paid for did not arrive in a usable state, and the store's recovery from the courier is their side of it.
A store that says "take it up with them" is giving you the wrong answer, and that is the point to escalate. If you are not happy with our answer
For sellers
Pack for the worst handling you have seen, not the average. How to pack an order
More: the wrong item was sent, how refunds work, how to raise an issue.