Just noticed you said they opened a case with Paypal.
Well, thats even more straightforward. You are covered under Paypal seller protecion, as long as you meet all their seller requirments, which are pretty standard. In that case all you need to do is provide proof of postage/delivery. If your address is registered and you posted it to the registered address then your covered. Even from unauthorised payments, not just not recieved claims.
Keep an eye on your accounts as sometimes they issue chargebacks, but everything is conected so its easy enough to reverse any.
Mark
Have included text from the Consumers Rights page for you;
PayPal Seller Protection
A buyer might make a claim, for example, with PayPal, if they believe that an item hasn't been received or the payment from their account is unauthorised.
They could open a dispute with the PayPal Resolution Centre, or they might issue a chargeback in order to get their money back.
If the buyer is making a false claim, sellers using PayPal are protected by PayPal Seller Protection and shouldn't lose out - provided that they've satisfied eligibility requirements.
Is your sale eligible?
For your sale to be eligible for protection from disputes and chargebacks with PayPal:
The item must be a physical, tangible good
The transaction should be marked - by PayPal - as ‘eligible’ or ‘partially eligible’ for PayPal Seller Protection on the ‘transaction details’ page, and in your confirmation email. If ‘partially eligible’, you'll be covered only if the buyer claims that the item wasn't received. You can find the 'transaction details' by logging into PayPal, finding the transaction in question and selecting the 'details' link
You must have posted the item to the shipping address on the ‘transaction details' page
The buyer must have paid in a single payment
Your primary residence listed on your PayPal account must be in the UK or Ireland
You must have followed all postage requirements.
Exceptions to PayPal protection
If you deliver an item in person or allow the buyer to collect it, you won't be protected by PayPal if the buyer opens a dispute.
If you've sold a service or a licence for digital content, you won't be protected, either.
Top Tips
To make sure your are protected by PayPal's Seller Protection, always keep proof of postage, and proof of delivery.
Remember, goods delivered or picked up in person, or posted to an address other than that on your 'Transaction Details' page, will not be protected from potentially false claims or chargebacks.
Postage requirements
If a buyer claims for an unauthorised payment, you must have proof of postage to be protected.
If they claim that an item wasn't received, you'll also need proof of delivery.
Proof of postage must be online or physical documentation from the postal company that includes all the following:
A status of 'shipped' (or equivalent) and the date of postage
The recipient’s address, showing at least the city/county or postcode (or international equivalent)
Official acceptance from the shipping company (for example, a postmark, receipt, or online tracking information).
Proof of delivery can be online documentation from a postal company that includes all the following:
A status of 'delivered' (or equivalent) and the date of delivery
The recipient’s address, showing at least the city/county or postcode (or international equivalent).
PayPal time limits
A buyer must open a dispute via the PayPal Resolution centre within 180 days of making the payment. This is an extension of the 45 days which it was previously. Buyers are encouraged to deal directly with sellers to resolve the dispute.
If a resolution can't be found, the buyer can escalate the complaint - but only within 20 days of opening the dispute. Otherwise, PayPal will close the dispute and the buyer won't be eligible for reimbursement.
During the claims process, PayPal may require documentation to support your position, such as proof of postage and delivery.
Once a dispute is escalated, PayPal will - after surveying the evidence - make a decision in favour of the buyer or seller.
If you've followed all the requirements for your sale to be eligible for PayPal Seller Protection, it's unlikely that you'll lose out.
PayPal and chargebacks
A buyer may choose to file a chargeback through their bank. Credit card chargeback rights may be broader than PayPal's terms and conditions - for example, they can be filed more than 45 days after payment and may cover intangible items.
If a buyer has opened a claim with PayPal and they then file a chargeback, PayPal will close their claim and the buyer will have to rely on chargeback rights.
PayPal and Ebay
Buyers paying via PayPal for items bought on Ebay are also protected by Ebay's Money Back Guarantee policy. It can be used for problem Ebay items, such as those not being 'as described' or not received.
Like PayPal, if a buyer files a chargeback with their bank, Ebay's Money Back Guarantee Programme will no longer pursue the claim.
There are differences between the eBay scheme and chargeback with banks, around timeframes and eligibility requirements.
And, again, a buyer can't seek resolution through PayPal and Ebay systems at once.