First, let me tell you how sorry I am for the loss of your dad. Having lost my own dad a few years ago, I know this can be a very difficult time for you and your family. I will certainly keep all of you in my prayers!
With regard to your specific question, pursuant to the Social Security administration (http://socialsecurityinfo.areavoices.com/2012/03/06/social-security-in-the-month-of-death-is-that-payment-due/):
"A: Social Security benefits are payable to a person only if he or she is alive for the complete month. This applies whether the person was receiving SSA retirement, survivors or disability benefits based on either their own earnings or the record of someone else.
To illustrate this, if a person receiving Social Security benefits dies during February, even on the last day of the month, no benefit is payable to that person for February. No partial payments are made for a month – either you are eligible for benefits that month or you are not.
Social Security benefits for a month are received the following month. Using the above example, SSA benefits received by this person in February were for the month of January and payable because he or she was alive all through January. However, the SSA benefit received by this person in March is for the month of February. It must be returned because he or she was not alive for the complete month of February. "
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