ALBANY — The city is getting one last chance to block enhanced-death benefits for the widow of a 9/11 hero cop.

The state’s Court of Appeals has granted the city police-pension fund the right to appeal lower-court rulings that held Frank Macri died from lung cancer caused by his work at Ground Zero.

The lower courts ruled that Nilda Macri is entitled to line-of-duty death benefits — her husband’s salary, tax-free — and Frank Macri will be listed as having died in the line of duty.

But the police-pension fund is fighting to uphold the determination of its medical board that Macri’s cancer was too advanced to have been caused by his WTC work.

Macri was injured by debris from one of the falling towers. He continued helping with the rescue and cleanup operations until early 2002.

He was diagnosed with lung cancer in 2002 and died five years later, at 52.