Update iPhone 4s From iOS 9.3.5 To iOS 10 Beta 8

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Apple released iOS 10 Beta 8, which includes a number of bug fixes and improvements.
You can follow these simple instructions to install or update iOS 10 Beta 8 on your iPhone, iPad or iPod touch.
Install iOS 10 Beta 8 update wirelessly Over the Air (OTA):
Before you start the download, plug in your device so the battery doesn’t drain during the update process. It can take anywhere from 15 mins to an hour for the update to download and install, depending on how Apple’s servers are handling the load and your internet connection. You may also want to connect your iPhone to your local WiFi network, so you don’t get charged for downloading the update over your cellular connection.

Once you are plugged in and connected via WiFi, open the Settings app and tap on General > Software Update. iOS will automatically check for available updates and will inform you that iOS 10 Beta 8 software update is available.
Tap Download to download the update. Wait for the download to complete and then tap Install to apply the update. If you get tired of waiting for the download to finish (it could take a while) then go do something else. Your iPhone or iPad will continue to download the update and will send you a notification when the update is ready.  Go back to Settings > General > Software Update and then tap Install Now to install the now downloaded iOS update file.
A note to Jailbreakers: if you’ve used evasi0n, OTA updates will be disabled, which is convenient if you plan to delay updating. If do want to upgrade, you’ll have to restore your device via iTunes as described below.
Install iOS 10 Beta 8 update via iTunes
Some folks prefer to physically connect their iPhone to a computer via a USB cable and update their phone via iTunes. Since you are not dealing with WiFI signal, there is less chance of an error occurring during the download and install process.  Before you plug in your iOS device. take a moment to make sure you are using the latest version of iTunes. Click on iTunes in the menu bar and then click  on “Check for updates.” You can also go directly to Apple’s iTunes download page, which is now allowing you to download iTunes 11.1.3, the most recent version of the media manager.

Once iTunes is all squared away, it’s time to turn your attention to your phone. Connect your iOS device to your computer using an USB cable. Wait for iTunes to open and connect to your device. Click on your device in iTunes and then click the “Check for Update” button in the Summary pane. If an update is available, iTunes will prompt you to download and install the update. Wait patiently and do not disconnect your device until the update has finished.
Install iOS 10 Beta 8 update using firmware file via iTunes
If for some reason, the iOS 10 Beta 8 update isn’t available via OTA update or via iTunes then you need to follow these instructions.

iTunes Link