The usual way of taking a screenshot in iOS by holding down the home key and pressing the power button does not work when on the power off screen, so I looked around a little to see if there was a way at all to take a screenshot in this scenario and turns out there is!
To do this, the assistive touch feature needs to be enabled. To enable this, go to Settings > General > Accessibility > Assistive Touch. Turn it on from there. This will bring up a little square button that can be moved around on the screen. This comes up on the power off screen.
To take the screenshot, press the assistive touch button, choose Device, More and then Screenshot. This will allow to take a screenshot of the power off screen as well as any other screens where the normal screenshot feature may not be available.
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