Just wondering, do points accumulated with Air NZ have an expiry at all, or do they stay on your account like with Qantas, so long as you fly or spend or have movement in your account every so often?

I've just booked a flight with LH and joined their Miles and More thing. But, I've since been thinking perhaps it would be better to join Air NZ (especially since I'm Australian and NZ is much closer than USA or Europe!). The flight I booked isn't until August anyway, but is it possible to somehow get the points for this flight (which won't be credited until the flight) over to an Air NZ account instead, once I sign up to Air Points? I understand air points dollars are different somewhat to LH M&M mileage points, but after all, they are both Star Alliance!