If there remains any act of administration to be done, other than making settlement and distribution or payment of legacies, and there is a remaining or succeeding executor or administrator, a decree must be rendered in his favor for the amount found due on such settlement, and for the delivery of any personal property in the hands of the executor or administrator whose authority has ceased or, if dead, of his personal representative; but if more than six months have elapsed from the original grant of letters and there remains no other act of administration to be done than making distribution or payment of legacies, and the estate is solvent, the court must at once proceed to decree distribution or payment of legacies directly to those entitled; or, if in the case last mentioned, there are money assets in the hands of the outgoing executor or administrator, or, if dead, of his personal representative, in excess of a sum sufficient for the payment of debts and expenses of further administration, such excess must be distributed, or legacies paid therefrom, directly to those entitled, without passing through the hands of the remaining or succeeding administrator.