And Hilton replies...
As a one time exception if you are the beneficiary of a member's estate and wish to assume responsibility for their points, you must provide us with the proper documentation that verifies you are the responsible party for the deceased. This information can be mailed or faxed to us at 972-490-3870, attention Priority Department. Please request for the account to be transferred into the appropriate name.

And Continental Airlines' response:
Only if it is specified in the will. We would need copy of that and the death certificate. If there is no will, we would send you a Hold Harmless Agreement Form to fill out and return noterized.