If you knew the fireplace manufacturer, you could try and research what piping they spec'd, then you could see if that piping manufacturer is still around and then get the remaining components to finish at top & below to stove.
Or do the same if pipe manufacturer is known and still around. Technically, the problem lies here....... each pipe manufacturer is tested to code with a system made of their components connected together to complete the system. To add another manufacturers components to another's, most likely voids the code compliance because it was never tested that way.
But, if you can find the right components that fit to get it run to the stove, it could be done. Not sure how a double wall would match up to a triple wall.
You could always tear that stuff out and run a complete proper set up. Its your house and family, your decision.
Sometimes when thinking dollars, you have to stop and think is any potential hazards worth a few hundred dollars?
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UGG UGG