How to remove activation lock?

She will need her Apple ID and Password to open Activation lock which is a theft prevention feature. We cannot help and Apple will not unless you can provide the original receipt clearly showing the serial number. Perhaps this link will help her remember her details.

https://iforgot.apple.com/password/verify/appleid

She needs to recover access to her iCloud account.

https://iforgot.apple.com

A factory reset will not work in this case, because she has to remember Apple ID and Password to get past Activation Lock.

Have your wife (assuming this is legit) put in her AppleID & password as the prompt is requisition and she'll gain access to her iPhone.

The only other option is to perform a phone reset (via iTunes) to erase the phone completely and restore it back to factory.

I didn't say to do the reset via the iPhone's own reset feature. One can enter recovery mode using iTunes, and perform a factory reset that way. All data is lost of course.

That will NOT bypass the activation lock.