Since this was interest earned after the date of passing, and since you are the beneficiary, you would claim the interest.
You can enter the 1099-INT as if it were your own.
"If you receive interest that accrued but was not paid prior to the owner's death, however, it is considered income in respect of a decedent and is taxable on your return."
TurboTax Link
Additionally, in your situation, there would have been no expenses or tax paid on this income by the decedent or the estate prior to you receiving it. Simply add the 1099-INT on your return and keep with your tax files.
IRS PUB 559
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