You need to contact the Housing Authority that covers the area you will be moving into and ask if they currently have any restrictions on Incoming Portability Vouchers. NY State Housing Authorities list is here:
All vouchers have the ability to port to another location but each Housing Authority can put restrictions on them due to funding. Once you find out if the Receiving (in NY State) Housing Authority has any restrictions and what they are you would then need to contact your caseworker (in NJ State) and ask if they have any restrictions on Outgoing Portability Vouchers and explain that you would like to Port your Voucher to the chosen Housing Authority (in NY State) and explain their restrictions.
Just because the Housing Authority is not issuing new Vouchers does not mean they aren't accepting Portability Vouchers. It's a separate issue as Vouchers porting in offset Vouchers porting out. People move in and out of different Housing Authority's jurisdictions all time as a Voucher holder can move anywhere in the United States where there is a Housing Authority administering the program.