Can you please try the same workflow with new catalog.
Click on File Menu << Create New catalog << Add two folders to it and try moving it within the Lightroom to the different location.
Let us know if that works.
After last update...
Exactly what update was that?
Lightroom version: CC 2015.3 [ 1052427 ]
Hi Mohit, I can move them without the issues on the main drive where the catalog sits but not on the external drive. Well, they move but they do not apear in the new location until I restart lightroom...