I'm sorry for your loss.
You would need to contact Apple support directly. I've never seen anyone post any instructions or linked to any Apple articles for transferring ownership of a device. About the only time you may need to prove ownership is if the Mac becomes locked & you want to ask Apple to remove the lock....and perhaps in some regions it may necessary to prove ownership before any repairs are performed. In the US proof of ownership is not usually required for repairs.
I did find this Apple article for transferring the AppleCare coverage (not quite the same thing, but it may give you an idea of what you may need to do):
Transfer your AppleCare plan - Apple Support
I did find this post:
Transfer ownership - Apple Community
If you cannot get an answer even from Apple, then make sure to retain the original sales receipt and make sure to also retain a copy of the death certificate so that you could possibly use them to prove ownership if it ever becomes necessary (such as having Apple to unlock the laptop). Sometimes it may be better just to wait & see if it is ever an issue. You may also want to ask the person in charge of the estate on how to proceed as well (especially if they are a lawyer).