The Pierre Auger Observatory is undergoing a major upgrade, called AugerPrime. One of the goals of this upgrade is to improve the capabilities of the existing stations of the surface detector. The main modification consists in the addition of a new scintillator surface detector (SSD) to each water-Cherenkov detector station. The large-scale production of the SSDs started in 2017. The detector assembly is done in six laboratories with the collaboration of many other institutions providing components. Each institution involved follows common procedures, making sure that all the high standards set by the design are being met. We describe these procedures, which include quality checks of all components and a final certification of each detector with cosmic-ray muons. The deployment of the SSDs at the Observatory is already under way.