The provisions of the law with reference to the compromise of taxes shown on the back tax book or recorded list of delinquent lands and lots in the collector’s office shall apply to and shall also authorize the compromise of any judgment for taxes after the same had been rendered therefor and up to that time when the property shall be sold under execution issued on said judgment; such compromise to be authorized by the same officials and under the same conditions as set forth under existing law for the compromise of taxes.