how to back up iPhone 11 with a black screen
How to back up iPhone 11 when screen is frozen black?
iPhone 11, iOS 14
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In order to perform a backup procedure (via wifi to iCloud or via USB to a computer), you need to interact with your iPhone's screen.
If it is frozen, try a "forced" restart of your iPhone, using these instructions:--> Force restart iPhone – Apple Support
If it is broken, have it replaced at an Apple Store or AASP.
Regards
Giulio