Updating iPhone 5s from iOS 7.0–9.1 to iOS 10.3.3 OTA

Some members of /r/jailbreak mentioned it's possible to update iPhone 5s to iOS 10.3.3 OTA by modifying SystemVersion.plistto contain iOS 7.0.2 data and erasing the device with Cydia Eraser so device will retrieve iOS 10.3.3 OTA update itself afterwards. However it turned out the latest Cydia Eraser 0.9.43 restores original SystemVersion.plist file and that method won't work.

There's a way to update OTA (over-the-air) to iOS 10.3.3 any iPhone 5s running iOS 7, 8, 9 version that supports only untethered jailbreak (iOS 7.0, 7.0.2, 7.0.3, 7.0.5, 7.0.6, 7.1, 7.1.1, 7.1.2, 8.0, 8.0.2, 8.1, 8.1.2, 8.1.3, 8.2, 8.3, 8.4, 8.4, 9.0, 9.0.2, 9.1) even if you don't have SHSH2 blobs for iOS 10.3.3. I've successfully tested this on 5s running iOS 8.1 and 8.3. You'll require a virtual machine (freeware VMware Workstation Player for PC or VirtualBox for macOS) or PC with Windows (to get direct ISO link of Windows 10 use Developer Mode of your browser on this page and set your browser developer screen resolution to mobile device, i.e. Google Chrome > F12 > iPhone 5). SHSH2 blobs of iOS 10.3.3 are not required so you can update without SHSH2 blobs. I can confirm iOS 10.3.3 is snappier than iOS 8.1 on 5s, g0blin jailbreak for iOS 10.3.3 is coming soon. It seems 5s performs poorly in iOS 11 so updating to 10.3.3 is generally a good idea.

You should first jailbreak your iPhone 5s that is running legacy iOS. Be sure to remove any current version of iTunes and install older iTunes 12.2 (except for evasi0n7 by spockers since it requires iTunes 12.4.3) for better tool compatibility. Disable Find My iPhone, Passcode Lock, enable Airplane Mode, make your 5s trust your computer and use the appropriate tool for jailbreaking:
iOS 7.0–7.0.6 evasi0n7 1.0.7 by spockers (incompatible with OTA-updated iOS 7.0.X) or evasi0n7 1.0.2 by spockers (probably compatible with OTA-updated iOS 7.0.X), iTunes 12.4.3 64-bit
iOS 7.1–7.1.2 Pangu 1.2.1.1 [direct link], iTunes 12.2 64-bit
iOS 8.0–8.1 Pangu8 1.2.1.1 [direct link], iTunes 12.2 64-bit
iOS 8.1.2–8.4 PP Assistant 2.5.1 [direct link, guide], iTunes 12.2 64-bit
iOS 9.0–9.1 Pangu9 1.3.2.0 [direct link], iTunes 12.2 64-bit
iOS 8.0–8.1.2 TaiG 1.2.1 [direct link], iTunes 12.2 64-bit
iOS 8.1.3–8.4 TaiG 2.4.5 [direct link] (incompatible with virtual machines), iTunes 12.2 64-bit

Note PP Assistant should be able to jailbreak any iOS from 7.0 to 9.1 and is a solid product overall. But you should strictly follow the guide because program is in Chinese. I recommend you not to waste time getting TaiG tool to work and use Pangu/PP.

Upon successful jailbreak of your legacy iOS, follow these steps:

Download and install iFunbox or similar PC program

Run Cydia, find and install Cydia Eraser, Apple File Conduit 2

Connect iPhone 5s to computer, launch iFunbox, find /System/Library/CoreServices/SystemVersion.plist and copy it to computer; you can also backup legacy iOS blobs – /System/Library/Caches/apticket.der

Edit your SystemVersion.plist copy with Notepad: set ProductBuildVersion to 11A501, ProductVersion to 7.0.2 (or use untouched iOS 7.0.2 file)

Enable Wi-Fi on your iPhone 5s, do not disconnect it from iFunbox

Here comes the tricky part. Cydia Eraser executes iOS restore in two stages: firstly it compares current state of every file/folder and looks what's been modified while system was jailbroken, secondly it downloads and places in user folder unmodified files/folders from Apple servers, thirdly it replaces modified files/folders with originals. The trick is to let Cydia Eraser complete scanning of your device and to manually replace SystemVersion.plist while Cydia Eraser hasn't finished it's job. You can have a look at how Cydia Eraser works. You should replace SystemVersion.plist with the modified one when the second status bar completes 80% (first status indicator is labeled "downloading bill of materials", you should pass it through). It's recommended that you first open /System/Library/CoreServices/ in iFunbox and try to copy and paste edited SystemVersion.plist in this folder so the "Replace or Skip Files" dialog would appear but you should click "Replace" only when second bar reaches 80%.

Once iPhone 5s reboots, you'll have to re-activate it with SIM card and Wi-Fi. At this point your device may act unstable and blank screen with Apple logo and loading bar may appear unpredictably. If you succeeded in changing iOS version, all icons on the Home Screen will be broken, blank loading screen may appear unpredictably. At this point you should open System Preferences and confirm your iOS version is 7.0.2.

In case Software Update dialog won't appear by itself use System Preferences > General > Software Update to get iOS 10.3.3 OTA update. If you failed, Cydia Eraser will simply bring your device to unjailbroken state and you can try again.

Note It's recommended that you install tvOS 11 Beta Profile so your 5s won't download iOS 11 OTA.

TL;DR
1. Jailbreak your current legacy iOS
2. Install Cydia Eraser and Apple File Conduit 2 from Cydia
3. Copy /System/Library/CoreServices/SystemVersion.plist to PC using iFunbox
4. Edit SystemVersion.plist using Notepad: ProductBuildVersion – 11A501, ProductVersion – 7.0.2
5. Enable 5s Wi-Fi, keep 5s connected to PC and /System/Library/CoreServices/ folder open in iFunbox
6. Start copying modified SystemVersion.plist from PC to /System/Library/CoreServices/ but don't confirm replacing original yet
7. Run Cydia Eraser and confirm replacing of SystemVersion.plist when second loading bar of Cydia Eraser passes 80%

8. Check for Software Update once 5s reboots

Source: reddit