Is it possible to update an iOS device to a version older than the current version?

To give a clear answer to the question that was asked, which is whether a device can be updated to the latest version of iOS it supports, even if that version of iOS is no longer current.

Yes, it is possible. Software Update, either on the device or via iTunes, will offer the latest version that is supported by your device.

I can't readily find an official reference for this but it is supported by numerous other answers to similar questions on this site.

Normally you should be able to update via iTunes (in this case, further information on that below).

If that doesn't work you need to look what model Nr. the iPhone is (something like A1429, for example) and download the appropriate iOS software (about 1 GB). By alt-clicking on the update-button in iTunes you are able to select a specific package you want to update from. Select you downloaded package and wait until the software ist installed on the phone. You should be able to install the most recent version of iOS for your iPhone model this way.

If you're experiencing any problems with this, let me know.