Bring the feijoas to a rolling boil in a pot, while mixing constantly. Meanwhile, wash the jars and lids with soap, place them on a canning rack in a tall pot, and fill the pot with room temperature water (at least an inch past the height of the jars). Bring the pot with the jars to a boil as well.
Mix the sugar and the lemon juice into the feijoas, and bring back to a boil.
Add the pectin quickly, bring back to a boil, and turn off the heat after 1 minute. Use a metal spoon to scoop out the foam from the top of the jam.
Place the jar lids in a bowl. Use a canning jar lifter to lift the jars out of the hot water, pouring the water into the bowl with the lids. For each jar: Place it on a towel, and use a funnel to pour the feijoa jam into the jar, leaving 1/8 inch of air at the top of the jar. Then, run a small spatula/bubble around the inside of the jar to remove trapped bubbles. Wipe the rim with a damp towel and place the flat lid on top. Loosely screw in the remaining part of the lid (not too tightly or the seal won't create properly).
Boil the water in the canning pot again, and then use the canning jar lifter to place the filled jars in the boiling water. Leave them in boiling water for 10 minutes, and then turn off the heat source. Let the jars sit in the water for an additional 5 minutes.
Remove the cans from the hot water and place them on a towel. You should hear the lid pop, meaning that a vacuum seal has been created. Wait 12 hours, and then check the seal by holding onto the flat lid only, and lifting the jar. If the seal remains intact, the jam can last for up to a year. Otherwise, the jam must be refrigerated.