Property Taxes paid while non-resident

No, for NJ state tax purposes you can only deduct the property taxes paid during your NJ residency.

From NJ Income Tax – Part-Year Residents: As a part-year resident, you report only the income you earned or received while you were a New Jersey resident. You must prorate all the credits, exclusions, exemptions, and deductions for which you qualify. That means you can take only that part of the full deduction, credit, exclusion, or exemption that represents the amount of time you were a resident of the state.

NJ's premise is that you paid the remaining balance of property taxes with income that was earned elsewhere and not taxed in NJ. As a general rule, you can only deduct items that were paid for with after-tax earnings - since NJ can't tax the earnings used to pay your NJ property taxes, they won't let you deduct that portion of the property taxes.