There is no policy that says you have to ‘re-send it again’. In fact, Amazon recommends not doing so since you have no way to document a second shipment on an already shipped order. The Amazon recommended process is to refund and have the buyer reorder.
We refund immediately (minus the shipping charged) upon receipt of the undeliverable package. If the buyer wants they can purchase again with a correct address, we email them stating why the package was returned and that we have refunded their order.
Not sure why you are emailing them. Are you asking if they want to have it reshipped, or ship to a different address? I would do neither of these because; 1) you would have to pay to reship at your own expense, 2) shipping would have to be purchased outside of Amazon which you cannot document and 3) shipping to a different address will prevent any protections from a claim since this is not allowed.
You should always refund upon a returned package as soon as possible.