Hi Christoph!
In PMBOK 5 we have:
4.3 Direct and Manage Project Work
Direct and Manage Project Work is the process of leading and performing the work defined in the project
management plan and implementing approved changes to achieve the project’s objectives. The key benefit of this
process is that it provides overall management of the project work. The inputs, tools and techniques, and outputs
of this process are depicted in Figure 4-6. Figure 4-7 depicts the data flow diagram of the process.
"Managing the approved changes" is the only logical choice for the question you cited. Once approved, the request moves into the purview of those responsible for actually making it happen.
Even if one thinks that updating the change request should happen after the change is completed, this would be a function of managing the change request, not of managing the change itself.
I hope this helps clarify for you!
Best regards,
Tracy