If the board of appraisers of a conservancy district finds that lands or other property not embraced within the boundaries of the district will be affected by the proposed improvement, or should be included in the district, it shall appraise the benefits and damages to such land, and shall file notice in the court of the appraisal which it has made upon the lands beyond the boundaries of the district, and to the land which in its opinion should be included in the district. The board shall also report to the court any lands which in its opinion should be eliminated from the district.