The colour of the building behind the Studentenbrunnen has become the iconic colour of the University of Bonn. The building was initially designed by a Bavarian architect as a four-winged palace for the Elector. Its foundation stone was laid in 1679. It was redesigned in Rokoko style and its interior was completed in 1755. Just 22 years later it was severely damaged by fire and rebuilt in a simpler style.
Its change of use came about in 1818 when it was gifted to the new university founded by King Friedrich Wilhelm III of Prussia. I am still sometimes surprised by how far west the Prussian Empire reached, I tend to think of it as being around and north-east of Berlin. Not next to the Rhein!
Some of the buildings suffered bomb and fire damage in World War II, and its three bells were removed to be melted down for ammunition. At the end of the war, two remained, albeit damaged and are now on display at one of the courtyard entrances into the main building.
When exactly the yellow colour was introduced is not clear, and it does seem to be limited to the former palace buildings in the middle of the city.
Ah, happy memories for your brother-in-law!