it sounds like the IPSW file format is corrupted. the customer might have run a beta or jailbroken version of iOS which can usually be 1 of many reason for error 51
delete the existing saved IPSW in the iTunes directory
- Launch Finder
- Click Go from the menu bar
- Scroll down and click ‘Go to Folder’
- Type in “~/Library” and click Go
- Click and open the iTunes folder
- Open the iPhone Software update
- Delete the.IPSW files
- Go to C:\Users\Your Computer Name\AppData\Roaming\iTunes\iPhone Software Update
- Find the.IPSW file and delete or you can press CTRL +A (control all) and hit the delete on your keyboard.
- Update the iPhone again.
- trying an update after this procedure should force iTunes to download a new file format
try downloading a fresh IPSW image currently Apple only sign 11.4.1 and Proceed to update the iPhone
hope this works if that doesn’t work. you might wanna give FoneDog toolkit IOS system recovery a try