First of all, both Copy and Import will honor any relationships.
per the ArcGIS documentation:
Any data dependent on the input is also copied. For example, copying a feature class or table that is part of a relationship class also copies the relationship class. The same applies to a feature class that has feature-linked annotation, domains, subtypes, and indices—all are copied along with the feature class. Copying geometric networks, network datasets, and topologies also copies the participating feature classes.
The error indicates you are copying in a feature class that participates in a geometric network, and that the geometric network includes the ArcFM solution object extension.
The question should be "how to copy a network with the ArcFM extension to a new database?"
use the ArcFM Object converter to convert everything to Esri Features before copying
Go through the process of enabling ArcFM on the target database so that it can house the ArcFM features you are copying into it. Follow the instructions here