As you may know, Social Security benefits are paid 1 month in arrears on the 2nd, 3rd, or 4th Wednesday of the month, depending upon your date of birth.
Therefore, based upon your husband's date of death on 9/7/2017, the payment received in September (for August) does not have to be returned to Social Security. However, since you must be alive for the entire month in order to be eligible for benefits for that month, any payment of your husband's benefits made in October (for September) would have to be returned.
You didn't indicate your age or whether or not you are currently receiving retirement benefits based upon your own earnings record or Spousal benefits based upon your husband's earnings record. Presuming for the moment that you are currently receiving Spousal benefits, you are now entitled to Survivor's benefits which will equate to your husband's full retirement benefit that he was receiving.
Since you can only receive retirement benefits based upon 1 earnings record at a time, you will receive only the Survivor's benefit, instead of the Spousal benefits you may currently be receiving.
The best way to proceed to file for your Survivor's benefits, is to make an appointment with your local SSA office and apply for your Survivor's benefits in person. That way, a Benefits Counselor will be able to answer any questions you have and explain exactly how your Survivor's benefits are determined. You will want to mention what you are making the appointment for so that the local office can tell you what you need in terms of documentation in order to confirm your identity (driver's license, passport, birth certificate, etc.) as well as a copy of your husband's death certificate, and any additional documentation of your marriage.
You will want to make an appointment rather than just "walking in" to your local office, as if you were to do that, the waiting time can be extensive and you may not be assigned an experienced Benefit's Counselor that you normally would with an appointment. Also, if there is a family member, a trusted advisor or close friend available to attend the meeting with you, that is a good idea as given the timing, the circumstances, etc., it is always better to have two people listening and making notes, which is valuable assistance at this difficult time.
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