cp -r -p SOURCE DESTINATION
cp -r --preserve=mode,ownership,timestamps SOURCE DESTINATION
These two commands do the same thing. The Second allows you to chose what remains the same. I am not aware of a way of specifically doing this with
mv, but I believe this is
mvs default behavior.
Alternatively, you could try copying hard-links, which is much more similar to
mv, as suggested here:
cp -p -r -l source/date target/
I believe the problem you are experiencing is due to an ntfs/fat partition? If this is true, try setting up a rule in /etc/fstab that uses your uid.