When the Governor-General is overseas, then the Administrator of the Government fulfills the Governor-General's functions.
The Administrator of the Government is the Chief Justice of New Zealand. In such cases the advice sheet must be addressed to the Administrator, rather than the Governor-General.
The Cabinet Office advises Ministers' offices and departments when the Governor-General is going to be overseas. Refer to the Cabinet Office Notices on the Public Sector Intranet for relevant Notices.