They can, and probably will, charge you. At 20%, there is too much cash there for them to waive it.
Here in Oz, anything under $1k is generally exempt, even for purchases. This probably saves a lot of work, but I'd also expect it to stop soon, especially if GST goes over 10% (I hope not).
I sent a laptop from my business address in Oz to my (same) business address in the UK. Customs tried to charge VAT @ 20%, even though it was obviously a used item, and actually several years old. It was cheaper to just ignore it and let FedEx ship it back, which is just stupid. Next time someone went to the UK, they took it as luggage instead.
I had the same issue sending 5 laptops (used for training) from the UK to Oz. Again, customs tried to charge, but I was able to prove that they were bought in Oz, and had GST fully paid. As far as I am aware, that is the only way to manage it.
So if you happened to have a UK receipt for that particular phone (and I'd never, ever suggest it might just be a receipt for any phone of the same model), you will probably be OK. Just tell them your cousin took it by mistake and is sending it back (a letter in the parcel could confirm this).
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