New Zealand Law
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Under New Zealand law, you need to have been in a relationship for at least 12 months before you apply for the partnership visa. So once you have been together that long he can apply and then move to New Zealand based on you being a NZ citizen and the 12 months together.
If you have been together more than five years then he can apply for New Zealand, but you would need to ask an Australian lawyer about the effect on Australia. He could not apply for residency in New Zealand but stay in Australia.
You have to be resident in New Zealand for 5 years before you can apply for citizenship.