XP Pro Folder Sharing

I need help.
I must be missing the obvious.

We have a domain.
On Gary’s Xp Pro computer he is sharing out G:\Goose.
In Properties ; Security ; he gave Everyone Full Control.

On Betty’s and Sam’s computers they mapped to G:\Goose.
When Betty elected to create a folder in G:\Goose the message ‘Access
Denied’
Looking at the Properties ; Security ; on Betty’s computer we see
Everyone with Full Control.

Returning to Gary’s computer in G:\Goose ; Properties ; Security ; we
add Betty. Betty is given Full Control. All boxes are checked. Now we
have Everyone, Full Control. Betty, Full Control.

Returning to Betty’s computer she is unable to do anything within the
Share G:\Goose..
Looking at Betty’s Properties ; Security ' we see Betty with Full
Control.

Sitting at Gary’s computer we had added Sam with Full Control. The
exact scenario is duplicated with Sam.

If we are adding users, giving them Full Control what is preventing
those users accessing Gary’s G:\Goose folder and files?

I thought sharing a folder, allowing Full Control, especially with
Everyone would solve any access issues. Thanks for any insight into
this problem.