(b) Absentee ballots received after the election commissioner has picked up the official ballots and other election supplies for the precinct are to be delivered to the election commissioner of the precinct who has been designated pursuant to section twenty-four, article one of this chapter, by the official designated to supervise and conduct absentee voting in person or by messenger before the closing of the polls, provided the ballots are received by the official in time to make the delivery. Any ballots received by the official after the time that delivery may reasonably be made but within the time required as provided in subsection (g), section five of this article are to be delivered to the board of canvassers along with the provisional ballots.