Looking at the aluminium piping, they have re-plumbed the twincharged system, i'd say this is causing idle and tuning problems, hopefully overcome by now. Lancia Delta S4 system was originally Filter -> turbo -> intercooler 1 - > supercharger (with bypass valve) -> intercooler 2 -> throttle body -> inlet manifold, i.e TURBO BLOWS INTO SUPERCHARGER. This Lancia appears to now have Filter - > supercharger - > turbo -> intercooler 1 -> intercooler 2 -> throttle body -> inlet manifold, i.e SUPERCHARGER BLOWS INTO TURBO. I can also see a supercharger by-pass valve in the air track after the filter so the turbo can get extra air when on song. From experience I'd say the engine is making boost at idle, which makes air pulsate and hard to tune. You need the supercharger bypass valve to be open slightly at idle so the engine can idle without boost. Difficult with the way it is now plumbed up. I'm not sure about the insides of the by-pass valve in the inlet tract (i'm guessing its like a 2-stroke reed valve), but ideally this needs to bleed some 'boosted' air from the blower back to the inlet filter at idle. I normally use a large throttle body with both vacuum and boost actuators to open it - works well. The by-pass valve needs to snap shut once the throttle valve is opened from idle so the boosted air heads to the turbo inlet. The same valve opens when the turbo is spooled up so the blower is by-passed. Hope you get it sorted.
Grazie mile Giorgio. The owner/driver was having problems with a flat spot (no power) then it would have a lot of power! There was a strong smell of fuel so maybe overfuelling? The car has no fuel pressure gauge but will be looked at soon.