Can't get iphone to install update

Hi! Trying to update my son's iphone (8), which was handed down from his older brother. In order to restore from backup, it says that we have to update to the latest iOS. He's currently on a version 13.3.1. But when we try to update, we get the "unable to check for update - an error occurred while checking for software update" message. So I went online and connected the phone to my PC, trying to update it via itunes. Thought it was working because it said that the updated downloaded, but now it's stuck in the "Preparing iphone for software update stage" and not changing. Any ideas on what to do. I need to be able to update in order to be able to restore the iphone from backup so he has all of his apps and data. Please help. We leave tomorrow for a trip and we need for him to have his phone operational.

Thanks!!