I have not died but a family member did and all airlines have an address to both fax or mail to where they need the death cert and a letter that states who the executor is, plus a note asking them to move the miles. So, mom wrote one saying please give X number of miles to herself and her three sons, for example, when dad died.
only delta said they wanted things notarized. All miles took only a couple weeks to post and with starwood, they also transferred the status but in all cases, you should ask.
also ask to have any upgrades moved over...
and, vouchers or coupons (as big of a pain these are to redeem) moved over to the new person receiving. Hey they may even extend their time limits--or maybe you can ask to have those transferred in to miles.
If you have suffered a loss, I am sorry to hear of it.