There are different requirements based on the length of the flight and how recently the cast was put on. It may need splitting etc. (usually for new breaks)
The most critical is the first 24 hours.
As other posters have said, it is because the limb will swell within the first 24 hours + you're at a reduced air pressure, all leading to a limb being constricted. Not good.
Since you're looking at 4 weeks then it *should* be ok. However, do not take my word for it, get your brother to contact the airline directly, explain when the break occurred etc and get the answer from them.