Hi and welcome to the forum Oystein,
I doubt that a dropshipper will honor their warranty in the way you described. From my understanding each dropshipper will have their own set of policies which you will have to check on before you use their services.
How drop shipping returns/ warranties are handled depends on the drop shipper's policy.
Many drop shippers will accept and process returns, replacing a faulty item with a new one, or issuing you with a refund if necessary (which you then pass onto the customer).
The drop shipper's policy will also inform you whether you should direct your customer to send the item to you for forwarding, or straight back to the drop shipper.
Make sure you check their returns policy on the drop shippers website before you start selling items, so you are clear what action to take.
You can learn more about drop shipping in our free education area:
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Hope this helps!