There are many options you can choose to benefit your child, if your child’s other parent has made you the beneficiary of their life insurance policy and has passed away.
For a child that is a still a minor, consider this: setting up a trust (with you as the trustee) with some of the funds from being the beneficiary, and put some of the funds in a bank account specifically set up to pay for the expenses of educating your child, as well as any other expenses related to your child.
If you are concerned with your child’s education, you might also set up a college savings account for your child with the funds you have received.
For a child that is not a minor any longer, you still have several options that are along the same lines. Consider giving them the money outright and letting them decide what to do with it. You will need to consult a tax advisor about this (potential gift taxes).
You can also set up a trust account with the money until a time you deem them responsible enough to handle the money on their own.
Of course, there are other options you could consider, but these are some of the best choices in general to benefit your child and your child’s future.