Dealing with all of the various assets after the death of a family member is difficult. I dealt with this with when my father passed away a number of years ago. It was painless to transfer the miles to my mother. Just call Continental and they should be able to help. I recall having to send the death certificate to them, but that wasn't unusual every bank, brokerage, etc needed them. Just get lots of official copies of the certificate.

Sorry for your loss.
Scott