The recent case of Xu & anor v IAG & anor  NZHC 1964 said that an insured home owner could not assign to a new owner the reinstatement rights under an insurance policy. The decision is subject to an appeal to be heard May next year. EQC in this publication on its website confirms that
Where an EQC claim is assigned, the assignee (the person receiving the benefit of the claim, for example a purchaser) will have the same entitlement(s) under the Earthquake Commission Act as the original owner. That means they will receive any remaining entitlement up to EQC’s cap for an event.