@mrsbv I'm sorry you are going through this. I am an administrator for some Facebook groups and closed and secret groups do not allow sharing. Public groups do allow it since the public can see all posts anyway, even if they are not a group member.
If there is a reason you cannot make the group private, I would include in each post that you do not want shared a disclaimer asking that the post not be shared. Even then, the public can still see your post since it is a public group.
Hope this helps some. Again, sorry you are dealing with this.