(a) If a new county is established, the commissioners court of the county from which the largest part of the territory of the new county is taken shall, not later than one month before the date of the next scheduled general election:
(1) divide the new county into convenient precincts for the election of justices of the peace and constables; and
(2) select convenient polling places in the new county.
(b) The commissioners court shall direct the county clerk to make a record of its actions under this section and shall transmit a copy of that record to the person who is elected county judge of the new county.