A few more steps...

iOS 16 beta profile has started downloading.

Make sure you open beta.ioslift.com in Safari browser.

You will see the following prompt:

Tap Allow from the popup.

Open Settings app - Profile Downloaded.

Then follow the prompts to install configuration beta in Settings app and restart your device.

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After your device has restarted, you can receive beta update in Settings - General - Software Update.

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Learn how to unenroll your devices to stop receiving developer betas ?