I'm Doug, and I'm so very for your loss. My goal is to provide you with excellent service today. Please don't confuse excellent service with a satisfactory outcome based on your wants and desires. I can only explain the law to you---not guarantee that you will be happy with the outcome.
Under present social security law, benefit payments are paid in arrears by one month---meaning that your September benefit payment is not paid to you until October. So, the payment that was received in October was yours to keep. However, if you receive any further benefit payments (such as one in November)---be they deposits to a bank account, a paper check received in the mail, or a deposit made to a debit card, you will need to return that benefit to social security. This is because a person is not eligible for a benefit payment for a given month if they do not survive through the end of that given month.
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I wish you and yours the best in 2016,