my father recently passed away. He was due to receive inheritance money from his aunt. He and my mom shared a j acct.

Please accept my condolences on the loss of your father. Unfortunately, no, your mother should not deposit his inheritance into a joint account which she held with him, as upon his death that account became 100% hers and his money should no longer be deposited into it. Your mother should take steps to open your father's probate estate, either by offering his Will for probate or seeking the appointment of an Administrator if he didn't have a Will. The estate will then receive the inheritance your father was to receive. Your mother may want to consider making a year's support claim, especially if there is no Will, but the check to your father should be deposited into his estate's account, and the estate should be properly administered to help ensure that any debts he may have had can be put to rest correctly and that the remaining inheritance assets, along with any other probate assets which remain after the estate has been fully administered, are distributed to the correct beneficiaries in the correct proportions.