(a) The commission shall transmit the certificate of adjudication or a true copy to the county clerk of each county in which the appropriation is made.
(b) On receipt of the recording fee from the holder of the certificate, the county clerk shall file and record the certificate in a well-bound book provided and kept for that purpose only. The clerk shall index the certificate alphabetically under the name of the holder of the certificate of adjudication and under the name of the stream or source of water supply.
(c) When a certificate of adjudication is filed and recorded as provided in this section, the county clerk shall deliver the certificate on demand to the holder.