1. The employee shall remain a participating employee in the retirement system established under chapter 201, laws of 1937, until the employee becomes vested in all of the contributions paid by, or on behalf of, the employee in the retirement system. When the employee becomes vested in all of the contributions paid by, or on behalf of, the employee in the retirement system established under chapter 201, laws of 1937, the employee may no longer be a participating employee in that retirement system and shall immediately become a participating employee in the Wisconsin retirement system. 2. The secretary shall pay, on behalf of the employee, all required employer contributions under the retirement system established under chapter 201, laws of 1937.