The method involves the ascertainment of at least the horizontal coordinates of at least one point of the cover device (140) on the shaft. An eg. concrete superstructure (4) is applied on an under-structure (3) and on the cover device. Removal takes place of the cover component and the part of the superstructure corresponding to the coordinates of the at least one ascertained point when the superstructure has reached its final degree of hardness. The cover device is installed on the cone (111) of the shaft. Before the installation of the shaft cover, at least a compensation ring (112) is placed on the cone.
