An assembly including a connecting member to be mounted on a first medical container, an adaptor including a gripping member to be mounted on a second medical container, a pierceable elastomeric piece, fixed with respect to the gripping member, a protecting envelope comprising a rigid shell substantially surrounding the connecting member and the adaptor in a storage position of the assembly, in which the connecting member is separate from the adaptor. The rigid shell is closed by a removable film. The assembly further comprises a first engagement portion for preventing the connecting member from escaping from the rigid shell when the film is removed. Also, a kit including such an assembly and first and second medical containers.
