I will be very thankful for any help.
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You would likely not have too difficult a time finding a job in New Zealand since, as you rightly say, there is a high demand for construction professionals at the moment, and there is likely to be for some time.
It may, however, be a bit more difficult to be granted permanent residency from the get-go, it is more likely that you would need to apply for a Work to Residence visa.
Have a look at our Visas for New Zealand and Working in New Zealand pages for more in-depth information.
Hope this works out for you.
Best,
Xavier