What is the ruling on an unintentional error in calculating a deceased person's financial dues, and the resulting increase in the amount owed, and is it obligatory to inform official authorities about this after the amount has been disbursed?

You must inform the responsible authorities at the university about the error in the جمع (collection/calculation) so they can rectify the matter, and obligate the heirs to return the excess amount or consider it a gift to them. This is because the heirs' silence and their benefiting from the excess beyond what their inheritor is entitled to is impermissible. You are not permitted to overlook what has happened, and the harm caused to some auditing officials due to your reporting of the error does not justify your silence, as you are the primary person responsible.