1) First the permissions for the Drop Box were different from an original Public folder onto another computer. Namely the "Custom" permission was missing.
After a short Google search, I was able to bring back the Custom Permission using Terminal: https://discussions.apple.com/thread/6496223
DO AT YOUR OWN RISK
Open Terminal and type: cd ~/Public/
Make sure the Drop Box folder is present in there: ls
You should see: Drop Box
If you see nothing there, make a new Drop Box folder: mkdir "Drop Box"
Change the permissions: chmod 733 "Drop Box"
Change the permissions again: chmod +a "$USER allow list,add_file,search,delete,add_subdirectory,delete_child,readattr,writeattr,readextattr,writeextattr,readsecurity,writesecurity,chown,file_inherit,directory_inherit" "Drop Box"
You now should see "You have custom access", Privilege "Custom" for the Drop Box Folder. (Apple + I, or Right-click /Get Info.)
2) Second, the Public folder shows as "Public" on the network as opposed to "User's Public Folder" which is more convenient.
After a second longer Google search, I found these:
I am not going to reproduce what's already there, again DO AT YOUR OWN RISK. For me the process worked beautifully! Cheers!