How to claim money in savings upon parents death

My boyfriend's mother passed away leaving no beneficiary on her savings. The amount is under $5,000 but it is still significant to help recoupe monies paid for funeral expenses due to a lapse of insurance policy. He is her only child and paid for the funeral hisself. How would he go about claiming the money? Can he/we file papers ourselves to obtain the money?

How was the savings account titled? If it was titled just in her sole name, then it is a "probate" asset. However, in most states if the total "probate" assets are under a certain amount (e.g. $50,000 in IL), then you can use a simplified procedure stating that you are entitled to the asset under thw ill or intestacy laws. And yes, the "estate" is presumed to be the source of funeral expense payments, so you have a right to be reimbursed from the estate for the expenses.