What I would do:
#1.) Go thought the iPhone setup and when you get to "Apps and Data", choose "Setup as new iPhone" and then when it asks to sign into iCloud, DO NOT SIGN INTO YOUR iCloud ACCOUNT! Sharing iCloud accounts is a bad idea. Create a new iCloud account for your mom.
#2.) On one of your Macs, create a user profile for your mother (even if she will never use it). Sign into her new iCloud Account. Make sure "Contacts" are turned on in the iCloud settings.
#3.) Make sure Bluetooth is turned on.... on the phone and on the Mac.
#4.) Pair the phone to the Mac in the Bluetooth settings (of the phone and/or the Mac)
#5.) On the Sony phone.... somewhere.... in the contacts or maybe in the bluetooth settings.... there should be an option to send contacts. Some old feature phones were good enough to even have an option to "Send All Contacts." Anyway.... you need to send all of the contacts via bluetooth to the Mac. I googled and found this manual for Sony phones:
http://www-support-downloads.sonymo...ansfer_contacts_using_Bluetooth_global-en.pdf
#6.) On the Mac, if you were signed into you the Mac user account you made for your mom, and it is properly signed into iCloud, and contacts sync is turned on on the computer, the computer should start syncing and uploading the contacts just transferred to the computer.... to the iCloud. Once the contacts are in the iCloud....
#7.) On her new iPhone... Go to the Settings and then the iCloud settings... make sure the "Contacts" toggle is turned on (green). If all goes as plan... the contacts should already be populating in the Contacts app of the phone! (Sync'd from iCloud)
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Hope it helps.