Hi Eric,
The short answer is yes, the Lessons Learned Register should be transferred to the Lessons Learned Repository in the Close Project or Phase process.
I'm not sure what procurement documentation PMI is referring to on p. 501 of the 6th edition PMBOK that would be transferred to the repository as a result of the Control Procurements process before the Close Project or Phase process.
The repository houses Historical Information from PRIOR projects. Updating a repository as a result of the Control Procurements process before the Close Project or Phase activities are performed seems out of order to me.
This doesn’t help for your exam . . .
I imagine this discrepancy will be rectified in the 7th edition of the PMBOK coming sometime in 2021. The 7’s focus will be on project outcomes (how to work effectively with opportunities and threats) rather than project outputs (Lessons Learned Repository).
This does help for your exam . . .
1) I had several answer sets on my exam that included Lessons Learned as one of the choices. It’s good that you are reading carefully about them:
• Lessons Learned Register vs. Historical Information
• Change Request vs. Risk Register vs. Lessons Learned Register
2) Know what a Lessons Learned Register is:
Lessons Learned on CURRENT projects should be written in the register as they are learned.
3) Know what Historical Information is:
Files, documents, correspondence, lists, registers, cost models, risk management activities, previous project performance and decisions, closed contracts, closed projects from PRIOR projects stored in the Lessons Learned Repository.
4) Know what a Lessons Learned Repository is:
Lessons Learned on PRIOR projects stored in a central location, a repository, that contains Historical Information (see above) for others to access on their projects.
Best advice: If you understand the above points 2, 3, and 4, you 'll be able to answer exam questions about the Lessons Learned Register and Repository.
I wish you the best, Eric.
-Lisa