Prepare a boiling water bath and 4 pint/500 ml jars.
Spoon the applesauce into the prepared jars, leaving 1/2 inch/12 mm of headspace. Use a chopstick to ease out any trapped air pockets and add more sauce to return the headspace to the proper levels, if necessary. Wipe the rims, apply the lids and rings, and process in a boiling water bath canner for 15 minutes.
If you have a tea ball, or a small swatch of cheese cloth, I’d recommend putting your star anise in it to contain those little seeds if they get dislodged at some point. It’s much easier to simply pull that and your cinnamon stick out that way instead of fishing around for pieces.