How to insulate prefab chimney interior wall - GreenBuildingAdvisor

I have had a roof leak around the chimney masonry which was apparently "fixed" by the previous owner while continuing to leak small amount of water into the wall by the side of the fireplace. This wall is now open to allow for replacement of the rotted studs, and I'd like to improve on the original insulation from the inside. On the other side of the wall is the open prefab chimney cavity - apparently just one layer of brick lined on the interior with some plywood and fiberboard.

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Insulation - GreenBuildingAdvisor

Insulation - GreenBuildingAdvisor

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Insulation - GreenBuildingAdvisor

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How to insulate prefab chimney interior wall - GreenBuildingAdvisor

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How to insulate prefab chimney interior wall - GreenBuildingAdvisor