Any teacher or school employee who is employed in a public school, who is covered by laws relating to a retirement fund or pension system maintained by any county, city, or independent school district in this state or the board of education thereof, and who accepts employment in a nonsectarian private school in this state attended by students who are eligible for grants from the state shall continue to be subject to such retirement fund or pension system and shall be entitled to all of its benefits, provided that he makes or causes to be made to such retirement fund or pension system the contributions required of and for the benefit of such teacher or school employee had he continued employment in the public schools.