How was he still in NZ?

Stuff reports:

The man who murdered a Christchurch sex worker arrived in New Zealand on a fake passport and was due to be deported.

Sainey Marong, 33, was found guilty of murdering Renee Duckmanton in the High Court at Christchurch on February 23. He strangled her during a dispute after having sex in the back of his car on May 14, 2016. He dumped her body on the side of a rural road the next day and set her on fire. 

Stuff can reveal Marong arrived at Auckland Airport on a flight from Hong Kong using a fake British passport on January 10, 2014. He destroyed the passport at the airport. 

I don’t understand how he was living in NZ?

If he used the passport to get entry into NZ, then surely they could detect it was a fake?

If he destroyed it before the immigration check, then he should not have been allowed in.

Possibly he claimed to be an asylum seeker, but if so why is this not stated?