a. The membership of the pension fund shall consist of:
(1) all persons in city-service, as defined in this subchapter, in positions in the competitive class of the civil service, who shall serve probationary periods, or who shall receive permanent appointments in the police force after the time when this section shall take effect; and
(2) all persons in city-service, as defined in this subchapter, who hold a position of surgeon of police classified in the non-competitive class of the civil service.
b. Notwithstanding any other provision of this subchapter or any other law to the contrary, in any case where a member who is eligible to retire for service is appointed police commissioner or a deputy police commissioner, he or she shall, while serving as police commissioner or deputy police commissioner, continue to be a member of the pension fund. For the purposes of this subchapter, a member serving as police commissioner or deputy police commissioner whose membership is continued pursuant to this subdivision b or whose membership is restored pursuant to subdivision a of section 13-262 of this subchapter shall, during the period of such continuance or restoration of membership, be deemed to be a member of the police force in the department and his or her service as police commissioner or deputy police commissioner during such period shall be deemed to be service in such force.