I forgot to make many pictures. But the frame is pretty straightforward: horizontal beams along the floor and ceiling. Vertical ones at the same distances that I measured from the original PAX closet in our bedroom.
Then I covered the frame with 20cm wide MDF to cover the gaps.
Nice detail: the toe kick is at the same distance as the the original PAX toe kick.
Because of the roof incline, I had to cut of the corners of two doors, which was a bit scary. (Would the construction of the door remain stable?)
So I glued a strip over the newly cut edge. The left most door is made out of a panel from a DIY shop, because cutting off the entire left side would remove the inner left beam and render that door unstable.
Because the walls are not perfectly perpendicular, the resulting surface is somewhat crooked, so adjusting the doors was (still is) a challenge.
On the inside, I added acoustic padding so that the ventilation noise is significantly reduced (appr. 30dB).