How your Fans can share your Post
You are posting to a private Facebook group, your members can't effectively share your post. They have to copy and paste because it's a private group.
However, let's say you want to share a new blog post or a free webinar and you want your members to help spread the message to their fans and friends.
First, share your post on your public Facebook Fan/ Business page. Then, from the Facebook business page, share your post to your Private Facebook group. Now, your members can freely share it because the post originated on a public page.