Chimney repair

Hello All,
I have a chimney that broke off above where the flue pipe sticks out above the chimney itself, if that makes sense. As it stands now The flue pipe sticks up about 2 or 3 inches above the chimney. The problem is, an extension that was used to make it above our lower roof had blown down in a storm.
The extension was made of terracotta and was about 3 feet in length. The flue pipe itself seems to be in good shape, So what I plan to do is get a stainless steel flue pipe, insert it about a foot or two down in the chimney and cut it to equal the piece of terracotta that fell down.
My concern is, will it be suitable enough to replace what was there as far as creating enough draft.
The existing flue pipe in the chimney is 8.5" square on the outside and approx. 7.5 " internally. Should I get a 7" pipe to insert down in the flue? I was looking at the chimney liner kits, but it's a bit of an overkill for what I need.
Has anyone ever done this type of repair yet?

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