Sure we got the cp
command to copy things. use it with the -a option to have all the permissions remain the same. Else the umask would jump in place.
Or use the mv
command which moves things. Like copy and delete in one go. You would not need the -a options (dunno if mv even has one).
Ups forget to chown the files so the user has acces to the files
chown otheruser:otherusersgroup ~otheruser -R
In Desktop enviroment this could be difficult cause you normaly would need root to access the root owned files.
Maybe acl's could work.
If you just need two directory to be the same wether its the root or the other user you might want to look into syncing the dirs. Maybe with rsync. run the syncing in a hourly cron job if that suits.