Good morning Richard,
I'm Doug, and I'm very sorry for your loss. My goal is to provide you with excellent service today.
Please know that this is not the social security administration that you are directing your question to. You posted your question to JustAnswer. I have been a licensed attorney or more than 30 years and I handle social security issues.
Social security benefits are always paid in arrears. This means that the benefit payment you may receive in April is for the month of March.
When a person who is receiving benefits passes, the benefit that is received from social security in the month they die is theirs (or the estate or surviving spouse's) to keep. However, social security only pays a benefit for a month in which the person is alive the entire month. So for a person dying in March, there would be no benefit paid in the month of April---and if a payment is made, it must be returned to social security.
You may reply back to me using the Reply link and I will be happy to continue to assist you until I am able to address your concerns, to your satisfaction.
I hope that I have been able to fully answer your question. Please be so kind as to rate my service to you. That is the only way I am credited for assisting you.
I wish you and yours the best in 2016,