Q: Move data from iPhone 4 to iPhone 6 w/o wifi

All,

I need to visit my mother-in-law to upgrade her phone, and I'm a little concerned it will be quite an endeavor.  I'm hoping the forum might have some recommendations to mitigate the potential issues.

My mother-in-law has a Verizon iPhone 4 that has not been touched since purchased in 2013.  I'm not sure what OS is on it, but I'd guess iOS 5 (we bought it when the iPhone 5 was already released).  I have a new iPhone 6 plus for her in my possession.

She does not have wifi at her home, so I have to try and pull this off "on an island".  I can setup a wifi hotspot with my own phone if necessary, but I'd like to save my data plan as much pain as possible (not to mention it would take forever).

It's my understanding that I cannot just back up her phone and restore it using iTunes because the iOS version is too old.  Is that a correct understanding?  With that assumption, I already downloaded the latest ipsw to my MBP's drive (iOS 7.1.2) in hopes that I could upgrade her phone and THEN back it up.  Is that correct?

I have packed an original 30 pin connector as well.

Any other hints or tips?  If someone out there could definitively tell me what iOS her phone has to be so I can backup and restore to iOS 9, that would be very helpful.

Thanks!

Ken