Q: OS X Server - Members of Staff do not share Permissions

You don't say what, if anything, has been done on the server to set the default permissions on the sharepoint in question.

In my (much later than your) version 5.x of Server.app this is done in Services > File Sharing > Settings. Then double-click on the sharepoint name to open a permissions window. It's now possible to edit its permissions, allowing both groups and individuals certain levels of access.

Managing these permissions can be tricky, and beyond the scope of this post — or my ability! — to explain properly. If your Admin isn't familiar with the topic it may be time to buy a third party manual (I recommend the "OS X Server Essentials" series by Arek Dreyer, available in iBooks).

It's also no bad idea not to mess around too much with the permissions on your live sharepoint. Instead set up a test folder and share that, then use it for experimentation. Lastly Apple has removed the old Permissions Inspector that used to be so valuable in testing who really has what level of access to stuff in a sharepoint. However there's a useful third party utility called TinkerTool System that can do that.

If by Staff group you mean the default POSIX Staff Group then this is the expected behaviour. POSIX permissions don't propagate. Rather than struggling with POSIX permissions use Access Control Lists (ACLs) instead. These are more granular, far reaching as well as being inheritable. Avoid using the Staff POSIX Group. Create another group instead, name it something like Company Staff and add users to it. Then edit the permissions on the Share. Select the plus Icon and add the ACL for that group. It will appear topmost in the window above the default POSIX users and groups and their permissions. Don't mess with these. Once you're  one propagate the permissions. Test access with a number of users and hopefully things will behave as you want them to.

You need to set up appropriate permissions and ACL's:

     http://www.techrepublic.com/blog/apple-in-the-enterprise/introduction-to-os-x-ac cess-control-lists-acls/

C.