If this is a forum or a forum topic then this might help: http://codex.simple-press.com/codex/faq/problem-with-post-edit-buttonow-to/problem-with-post-edit-buttonow-to-configure-simple-press-with-membership-plugin/ – and it will really require a separate user group on that forum.

If not a forum or topic then there is nothing to be done in SP for this.