This guide has information about post editing permissions in the PublishPress Authors plugin.
By default, PublishPress Authors follows all the standard rules for WordPress permissions. If someone has permission to edit a post before PublishPress is installed, they will still have the permissions after installation.
If a WordPress user is selected to be one of the authors of a post, they will have the permissions to edit that post. There is one exception to this: Authors who are in the “Contributor” role can only edit posts if they have not been published. This follows the normal core behavior in WordPress.
So in the screenshot below, all three users listed in the “Authors” column will have the ability to edit this post.

