I would be sure to keep the phone until you have closed out all her accounts. You may need it for logging into her social media, financials, etc. Perhaps you could switch to a cheaper or a pre-paid without a lot of minutes, or transfer to google voice (not sure if that will erase her VM).
Otherwise, be sure to back up everything on the phone. Save the VM recording and all the photos. Take it to a phone store if you don't know how to do it.
I like PP's idea about giving the granddaughter a grace period if you choose to turn off the phone. I am very sorry for your loss.