Is the iOS image saved by iTunes for restoring the same for all iPhone models?
Each individual model requires its own restore file, known as an IPSW [iPhone software] file.

That also applies even to slightly different versions of the same model,. such as the US SIM &amp; non-SIM versions of the same phone.

You can see them listed at sites such as https://ipsw.me - which is just a list of redirects to the actual Apple downloads.

If you have a poor connection, or need the exact same download for more than one iPhone on more than one computer, you can get them via these links, then manually drop into place. They live in ~/Library/iTunes/iPhone Software Updates