Messages can be moved from one message box to another using a small helper job. All that is needed is a new job definition with a DelegatorJob.
This DelegatorJob is then parameterized as follows:

1. Destination job: here you set the job that the messages would normally go through when they end up in the destination message box¹⁾.
2. Start job immediately: No
3. Outgoing messages: No
4. Move message: MessageBox.Name

This job can be applied ad hoc to selected messages regardless of which message box they are in. The messages handled by the job will end up in the message box set above.