Set permissions for sharing only user through terminal
I solved the probelm by setting the permissions in the following way:

sudo chmod -R +a "user:USER_NAME allow list,search,readattr,readextattr,readsecurity,file_inherit,directory_inherit" PATH_TO_DIRECTORY/


This does the trick of changing the folder permissions so it propagates the users permissions automatically when new files are added. In this example

allow list,search,readattr,readextattr,readsecurity


are copied from the permissions of the sharing only user, and I have added

file_inherit,directory_inherit


in order to allow the files and directories within the original directory to automatically inherit the permissions.