Fireplaces, Heating Stoves, Flues and Chimneys - Damaged cleanout cap

I have a wood stove that vents through the wall and out an external metal chimney. Being the son of a fireman, I clean it out every year by removing the cleanout cap from the bottom of the vertical chimney pipe. Using my handy chimney sweep brush, I get rid of all the black junk that has accumulated from the previous year. This time, though, I yanked off the cleanout cap and a piece of the chimney came off with it. Oddly, it is a short single walled piece that looks like it is just an extender to hold the cap on. Problem is, I can't get it to go back on. I pried the cap itself off the metal extender and replaced the cap directly into the double-walled chimney. It seems to be on good and tight. But I don't want to burn down my house if the metal extender is somehow necessary. I searched online for something that looked like my system (house is about thirty years old, but the wood stove/chimney is almost certainly an addition), but didn't see anything like my extender. If anyone has experience with this, I would appreciate advice.