Apologies for the little confusion here, but you firstly say you inadvertently sent a refund, so informing that the wrong buyer was refunded ? Then, you say you have refunded the correct Buyer?
If you have made a correct refund and the buyer is asking where ' is their ' refund' , inform them that refunds go back to original payment source, and it's not always instant.
If they paid with a credit card, it can take up to 30 days, a full billing cycle for the refund to appear back in that card account.
Payment by bank card... up to 12 days to appear back in their bank account.
@brucie1966