So sorry Todd! Here is what generally needs to be done (and you do not have to pay extra for phone consult, they get pricey in my office). Yes, you want to notify the SSA of his passing so that they properly stop those checks. If he died in Dec, he was elgible for payment for November, which is the check he received THIS month, in Dec. But he won't be eligible for January check, as that is due for December and he did not survive December so can't be paid for Dec.
Your mom, should then apply (I'd do all this in person at the local office) for a survivor benefit, if it is greater than her own - she can take the highest of the two (but no longer will there by 2 check amounts, just one). She will also want to apply for the death benefit, a one time payment of $255, for what that is worth.
She should bring with her: Her own photo ID, her marriage certificate, his death certificate, her Birth certificate.
You should be able to cancel the Medicare at the SSA office. It WILL be out of his Nov. due/Dec paid check, since he had coverage then. Your mom's own Medicare will come out of whatever check she ends up getting, survivor if his work record was stronger than her own.
Again, I am so so sorry about your loss. I wish you both great strength and peace.