Performing a Design Copy on an object does not link the referenced objects to the Project.

Performing a Design Copy on an object does not link the referenced objects to the Project.

Performing a Design Copy on an object does not link the referenced objects to the Project.

This appears to be a limitation in the Design Copy function.

Please see Dassault BR Article #: BR10000008511

In order to work around this a custom script could be developed that will attach the related objects to the Project.

Or you can use Project Based Authorizations.  If you perform a Design Copy on a structure that is Linked and Secured to a Project then the related objects for the new structure will be Linked and Secured to the Project.