Move Message button

It's working as expected here. See if updating Mojave fixes the problem: Download macOS Mojave 10.14.5 Combo Update.

Please do the following before installing the update:

1. Shutdown the computer, wait 30 seconds, restart the computer.
2. Disconnect all third-party peripherals.
3. Resetting your Mac's PRAM and NVRAM
4. Reset the System Management Controller (SMC)
5. Start the computer in Safe Mode, then restart normally.
6. Repair the disk by booting from the Recovery HD. Immediately after the chime hold down the Command and R keys until the Utility Menu appears. Choose Disk Utility and click on the Continue button. Select the indented (usually, Macintosh HD) volume entry from the side list.  Click on the First Aid button in the toolbar. Wait for the Done button to appear. Quit Disk Utility and return to the Utility Menu. Restart the computer from the Apple Menu.
7. Repair permissions on the Home folder: Resolve issues caused by changing the permissions of items in your home folder.

When I click the "Move Message" button, I get a list of generic areas to move to (e.g., "Drafts".) Then I get a specific mailbox for each account I have set up, which requires clicking on the right arrow as shown here.

Once I choose a specific mailbox in a specific account, the move is accomplished.

Daniel Quinones wrote:

What I just noticed is that the command does not seem to work when I am viewing the message after having clicked on the alert of its arrival.

Yes, there is a lag between when you are notified of a message's arrival and the time it becomes properly situated in a mailbox area on your computer.

At the very bottom of the mailbox list on the left, a status indication often appears showing the movement of mail to/from different areas. Pay attention to that status indication, and don't attempt moves until all is quiet.