You can accrue SQ PPS and credit to another Star FFP. You just can't accrue KF miles or elite miles and credit to another Star FFP. If you have a SQ KF account there's an area in your profile to add your partner airline FF numbers. Add your NZ one in (or any other SQ FF partner) and any SQ flights where your partner FF number is in FQTV, it will automatically accrue PPS value in addition to the other airline miles/status points if you've added it in your profile.

EG: You have a SQ KF account. Add your NZ account number in as a partner account in your KF account profile. Fly SQ in J with your Airpoints number into the booking. You'll get NZ status points and APD as per partner airline earn rate, and then about a week later your SQ account will reflect the PPS value.