I deleted my Public folder from my User account, then I had to re-create it, with the Drop Box folder inside it. But it didn't behave properly.
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!