Is it possible to move a RQM Project to another lifecycle project?

It is not clear whether the other lifecycle project has RQM project or not.
For the wrong lifecycle projects between RTC and RQM, you need to go to RQM admin page to clear the association first. Then you may go to lifecycle project creation page and create a new lifecycle project, and for RQM, Use "link to existing" to select the existing RQM PA and for others, try to select the existing RTC and RRC project areas(suppose another lifecycle project has no RQM project or RQM project association was removed):

https://jazz.net/help-dev/clm/index.jsp?re=1&topic=/com.ibm.jazz.platform.doc/topics/t_creating_aggregate_projects_from_template.html&scope=null

Or try more direct way:

1) In the existing RQM project(the one you want to move), clear the existing association in RQM Admin page
2) Remove the existing lifecycle project's RQM association with its RTC and RRC(so that you can add 1)'s RQM into the lifecycle projects.
3) Go to 1)'s RQM admin page and then add necessary association manually with the target RTC and RRC(existing lifecycle projects)

Something similar to JKE Banking example as reference if you want to do it manually: