Disable Feed Post Editing for All Users

By default, all users who are assigned a profile that has the feed post editing permissions enabled can edit their posts and comments. You can disable feed post editing for all users in your organization, regardless of their assigned user profile.

User Permissions Needed
To enable or disable features in Chatter Settings: “Customize Application”
  1. From Setup, click Customize | Chatter | Settings.
  2. Click Edit.
  3. In the Post and Comment Modification section, deselect Allow users to edit posts and comments.
    Post and comment modification
  4. Click Save.

The feed post editing feature is disabled for your entire organization. Users can no longer edit posts and comments.