Hi, thanks for using JustAnswer.com I am Cris.
Have you tried to restore the phone through iTunes?
Well that is performing the update.
You can restore the phone but that will erase. If the phone is backup'ed through iCloud or iTunes you can restore it. But if you do not have a backup and don't want to lose the info you will need to do the update and yes will require a stable connection to at least download the update. Then after it is downloaded internet is not required for it to install.
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I wanted to follow up with you and see how did you make out? Also, if you had any further questions.