Step 4 in the move process is waiting for the destination vault stores to have completed the backup which involves setting and clearing backup mode.

Step 4 can be skipped to speed up the process by modifying the config file.  The administrator should be aware that EV will not wait for the moved items to be backed up by using this configuration.  

The setting is: 

Setting: WaitForBackupMode
Default: 0.
Values:
0 - always wait
1 - as per destination archive's Vault Store safety copy setting
2 - never wait

Steps: 

1. Browse to the Enterprise Vault install directory

2. Make a copy of the file EvMoveArchiveTask.exe.config

3. Remove the previous content of the config file and Copy the following content in EvMoveArchiveTask.exe.config.

4. Restart all the Enterprise Vault Services on the destination server.

5. Restart Move Archive Task in the right pane of Tasks.

6. Retry the task in Move Archive Status window.