Hi John,
You cannot move a post from one group to another, or from the home page to a group and vice versa. We are considering this in the future, but the decisions are not made yet.
Currently, there is an option to make it mandatory for your users to post only on groups, and not on the home page. You need to go to the Admin Panel> click on Group under the App Settings> and turn of the toggle at the end of the settings page "Users can post to community homepage" and save the changes.