The EIN is used on their estate tax return, Form 1041.
The SSN is used on their final personal tax return, Form 1040.
For more information about the taxes of deceased tax payers, follow these links:
IRS on
Deceased Taxpayer
E-file
Deceased Tax Returns
https://turbotax.intuit.com/tax-tips/family/death-in-the-family/L5albFXM4
I am sorry for your loss.
