A certified copy of the decree in a case of a mistake in the owner's identity shall be certified by the clerk of the court to the clerk of the county having possession of the “drainage record” book of the district, and the clerk shall copy the decree on the drainage record book as a part of the records of the drainage district, and file the decree among the papers in the cause in which the drainage district was established. The county clerk shall also certify a copy of the decree from the drainage record book to the trustee of the county charged with the collection of the assessments against the property affected by the decree, and the trustee shall note the changes on the trustee's “drainage assessment book”, which has been made out and delivered to the trustee by the county clerk, and thereafter collect the assessments on the property according to the changes so made in the decree.