How to sort this mouldy wall before dry lining

Hi,

Today I decided to pull down the old built in wardrobes from our main bedroom. They were on the exterior, east facing, wall and probably there for decades (I'm only here a year). I was expecting that there might be mould but what I found seems to be almost uncleanable. I've given it a quick spray of HG mould spray but it doesn't seem to have done much.

I am not sure what to do with it to be honest. My plan is to put cosy board on this wall and then a built in wardrobe on perhaps 1/3 of it, not the whole wall. If I kill it with bleach or vinegar could I just throw the cosy board over it? Or does it need to be fully cleaned for it to stop growing again?

FWIW I am pretty sure I've addressed / mitigated the root cause - I had some mould in another room which is gone and has not come back