The provisions of this part extending rights to a member of this system, or subjecting him or her to any limitation by reason of his or her membership in a county retirement system , shall apply in like manner and under like conditions to a member of this system by reason of his or her membership in any retirement system established under Chapter 2 (commencing with Section 45300) of Division 5 of Title 4 with respect to which an ordinance complying with Section 45310.5 has been filed with and accepted by the board or by reason of his or her membership in a retirement system established by or pursuant to the charter of a city or city and county or by any other public agency of this state and that system, in the opinion of the board, provides a similar modification of rights and benefits because of membership in this system and with respect to which the governing body of the city, city and county or public agency and the board have entered into agreement pursuant to this section. An agreement under this section shall provide that the governing body shall modify its retirement system to conform to any amendments to this part affecting a member’s right because of membership in a county retirement system , and may contain other provisions consistent with this section as the board deems appropriate. This section shall apply only to a member whose termination and entry into employment resulting in a change in membership from this system to the other system or from the other system to this system occurred after the acceptance by the board or after the effective date specified in the agreement. However, provisions relating to computation of final compensation shall apply to any other member if the provision would have applied had the termination and entry into employment occurred after the acceptance or determination by the board.