As this is described, it makes little sense. It should not be happening.
try again:
1. Drag the file from Finder window showing it on DownloadDrive/SomeFolder onto the Finder window showing TargetDrive/NewSomeFolder
2. Wait until copy is done. This may take serious time if file is large. Did you get any report that there is permission problem or some other issue? Does the file show in its new location?
3. Check the file is really in its target location = open it and try to use it. Does it work? Is it usable? Select file and hit cmd+I, it will open Info window. Is the Kind there appropriate file or is it shortcut?
4. Move the file from DownloadDrive into Trash. Do you get any complaints about permissions?
5. Empty Trash. Do you get any complaints about permissions?
if all these steps pass successfully, file has been safely moved and verified. If not, let us know here which step failed and how. You may need to fix permissions...
If you get permissions problem (most likely what I expect from that description), you need to check who is the owner of the file, all associated folders and drives etc. Google "change ownership on macos". You WILL need likely admin password for that. Which reminds me - are you running as admin?