In the trough of the home page, I am missing the messaging icon.
In the trough of the home page I am missing the messaging icon. How do I get it back?
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The Messages app is not one of the apps that can be deleted but it can be removed from the home screen. Go to the App Library (swipe left past your last home screen). From there you can touch and hold an app and add it to the home screen.
Also note the Search window at the top of the App Library.
If by "trough" you mean the Dock at the bottom of the screen, you can drag the icon back to it.
Also see: Move apps and widgets on the Home Screen on iPhone - Apple Support