Prepare medium or heavy syrup and add 1/4 cup bottled lemon juice to each quart of syrup.
Peel firm ripe papaya, remove seeds, cut into cubes, and gently cook in syrup for 2 to 3 minutes.
Pack hot fruit into hot jars and cover with boiling syrup, leaving 1/2-inch headspace. Remove air bubbles, readjust headspace, wipe rims, and apply two-piece lids.
Process hot-pack pints for 15/20/20/25 minutes and quarts for 20/25/30/35 minutes at 0–1,000/1,001–3,000/3,001–6,000/above 6,000 ft.