Hello Matt,

For copying individual modules and/or artifacts between different RM Servers, using ReqIF is the most common procedure.
You can do this from the 'project properties' >ReqIf tab, where you first need to create a ReqIf definition, add the things you want to copy, then create a ReqIf, download it, and import this into the target component.

Note:
In order to avoid duplicate artifact types, attributes, data types and list items in the target project/component in case you already have ones with similar names, it is adviced to set RDF URI's for these in both the source and the target.

ReqIf will copy:
-  all artifacts with their embedded artifacts and  modules with its complete structure
- Folders where the artifacts included reside, if you select this option.
- Views if you select any (note this will not filter the attributes of the artifacts, it will simply export the view itself, not its content)
- links between artifacts, if you select this option. ( Note that links will only be copied if the RM artifact at the other side of the link also resides in the ReqIf. In newer DNG versions the links will be re-established when copying the RM artifact at the other side of the link at a later stage as well).
- Artifact types, attributes and data types
- Tags if you select these.

This option will not copy the artifact history.

See also https://www.ibm.com/support/knowledgecenter/SSYMRC_6.0.5/com.ibm.rational.rrm.help.doc/topics/t_reqif_intro.html