I took the corrected birth certificate to register Muriel as a foreigner. I was told that the B permit would be issued automatically and I don't need to do anything. I was sure that I was not understanding what I was being told, but I left. A week later I got a postcard indicating that the permit was ready and I need to bring my passport and and work permit when I go to pick it up.
The permit was ready and I was out of the office in less than 5 minutes.