How old is the child? If the child is 18 or under than that child as well as his mother are entitled to survivors benefits. I have to do some research but I don't think they can get back payments from SSDI after they are deceased. . Let me do a little research and I'll be back. File right away because sometimes they figure benefits from the time you apply, not necessarily from the time the person dies.

How do I apply for benefits?

If you are not currently getting Social Security benefits

You should apply for survivors benefits promptly because, in some cases, benefits will be paid from the time you apply and not from the time the worker died.

You can apply by telephone or at any Social Security office. We will need certain information, but do not delay applying if you do not have everything. We will help you get what you need. We need either original documents or copies certified by the agency that issued them.

Here is just some basic info:
http://www.socialsecurity.gov/pubs/10084.html#3

Another Link:
http://ssa-custhelp.ssa.gov/app/answers/detail/a_id/395