Why has my friend's Clematis got mildew

The mildew you've described occurs most commonly because the plant is suffering from drought.
These are very thirsty plants and when planted in warm weather will need watering well every other day (i do mine daily!)
The glass roof will have reduced the chances of rain getting onto the roots and she should have watered it daily then for several months until the roots were down deeply.

I'd suggest moving it out into an open area where the rainfall can get to the roots very easily.

There's yet another thing to think about too .... is there now sufficient movement of air around these plants ? .... if there are a lot of plants around there they'll EACH need lots of air movement or they'll go mildew because of this too.

I sound all doom and gloom don't i ?
That plant will bounce back once the rain gets onto it directly :)

More questions - does she know which pruning group the Clematis belongs to? Or its name?

They do need to be pruned in the spring - how hard depends on the group. This will help the plant next year.

After it has been pruned, it should be fed...I use blood, fish and bone after pruning, and liquid feed the rest of the year in the growing season.

Fungicidal treatment spray for the mildew, but I wonder whether the air flow is sufficient for the plant now that is has a roof over it - it might be better to re-site it out in the open. Stagnant air encourages moist conditions which in turn encourage fungal infections.

Remember as well that clematis like their roots to be cool. I would be surprised if this is the case under a glass roof.