On behalf of the school board of a school district, on behalf of a governing board of a charter school under s. 118.40 (2r) or (2x), and on behalf of the governing body of a participating private school, as defined in s. 118.55 (1) (c), the department of workforce development shall pay to the department of public instruction the costs of tuition for a pupil who attends an institution of higher education under the program under s. 118.55 as provided under s. 118.55 (5) (e) 2. and 3.