All members of a local system included by contract in this system thereupon become subject to this part and cease to be members of the local system. Payments being made to persons who have retired or their survivors or beneficiaries under the local system on the effective date of the contract, or any subsequent amendment thereto, shall be continued and paid by this system at the rates existing on that date under the local system unless the agency elects in its contract or by amendment thereto to provide a recalculation of retirement allowances for persons retired under the local system on the basis of the provisions of the contract. The liability for those payments shall be included in the computation of the prior service liability of the contracting agency. All members of the local system who are members under provisions continuing membership after termination of service shall be deemed members of this system under Section 20731 with credit in this system for all of the service with regard to which membership was continued under the local system.