Authentication when moving files/folders on my external drive

Hi, there!

I am using two external hard drives on my mac – one for my everyday files and the other for TimeMachine of these files. But a few weeks ago I dropped high the HDD with my original data and he stopped working, of course. I has a guarantee and I replaced the HDD for a new one. After that I have one TimeMachine disk and one completely empty new disk.

To safe my files I decided to clone not all from the Time Machine but only files and folders from "Latest" folder with Carbon Copy Cloner to the new disk. This task finished successfully. But!

Now when I opening the new disk with my cloning files I need to type my password for every single action I want to take – move files, copy-paste files, create or rename folders… Even more – when I open some working file in some Adobe tool and click on Save button, it appear message "You do not have write access to the directory where the project is located."

Then I started reading the forums to learn how can I disable this. Everywhere recommend to open Get Info window of my new drive and change Sharing & Permissions to Read & Write privilege. Also unlock advanced options to check "Ignore ownership on this volume" and click on the small gear icon to take "Apply to enclosed items…" option. Some peoples also recommend to open Disk Utility and click on "First Aid". I did all of these, but there is nothing help!

Something interesting that I found was that when I create couple of folders on my Desktop and manually copy-paste files from cloned drive to that folders, files work properly, but if I copy entire folders to Desktop, the Authentication problem appears! It seems like the problem is with folders, not with files.

Fortunately, I did not delete anything from the other drive and now and I can start all over again. But is there a simple way to repair this?

Thank you!