Installing Freestanding Pellet Stove with Existing Chimney

[ylomnstr]

So I'm converting my free standing fireplace to a free standing pellet stove. Currently, the fireplace has what I think is a Class A chimney. From what my dealer told me, I can use 3" pipe from the pellet stove to the ceiling, and then use an adapter, and continue to run the 3" pipe through the existing class A chimney. Do I really need to do that? Or once I hit the ceiling and use the adapter, can I use the existing chimney and not have to run more pipe all the way through? Seems a bit odd to have to run pipe through the existing pipe. I'm attaching the St. Croix install file. My scenario is on the right hand side. I don't see any other pipe running all the way out the roof after using a PL Vent adapter at the ceiling. Above that, the chimney seems to stay the same.

Suggestions? Thanks.