Sorry to hear about this loss. I really hate people that seem to need your stuff more than you do!
I don't think that the serial is digitally in the processor. At least I have never seen any hardware utilities show it so my guess is that feature does not exist. One of the cool things Apple products do is have a serial that can be tracked digitally. Many android phones do this to. I think it would be great feature to add to CPUs in the future.
You can ask AMD support to be sure: https://www.amd.com/en/support/contact-email-form