Hello, after macrium is done with cloning, the "close" button is not appearing - I can only hide the window:

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Did you try using the little bar in the far right hand lower corner to minimize all Windows and try changing focus back to the Reflect window?  I've encountered a few times where the Close button doesn't appear in a Reflect window until I do this.

I did and then the second green bar was animated but the close button didn't appear. Actually it is not a problem at all if I can be sure, that the backup was done successfully. Is this the case?

Try the CTRL+ATL+M combination to bring up the last executed action log window.  See if that tells you if the backup completed.

Yes, the clone is done.  It says "Clone completed successfully" in the activity log.  Not sure why the Close button is missing.  I too thought it might be ReflectMonitor, which is summoned by pressing Ctrl+Alt+M, but it doesn't look that way since there's on File menu in the upper-left corner.

Ah, looks like the user is using a German language edition of the software.  Could be anything, as that version seems more prone to bugs.   

However the log content is in english - I've seen the message about completion of the backup, but wasn't sure if it is in fact completed.

The log itself is just HTML, I believe, being displayed by the application.  The button failing to appear has German text, which means the button itself, part of the actual application, was at fault.

With the window you want closed active, try Alt+F4, standard Windows keyboard shortcut to close the active program.

Failing that there's always task manager > end task.