Any city officer whose term of office began after the establishment of the retirement system and who did not become a member of the retirement system when his term of office began, shall be permitted to become a member of the retirement system at any time and receive a retirement allowance based upon service as a city employe rendered after such date of membership: Provided, however, That if membership is consummated within one year from the beginning of such term of office and such sums as would have been deducted from his salary had he become a member at the time of the commencement of such term of office shall have been paid into the retirement system, he shall thereupon become entitled to all the rights and privileges in the retirement system as would have been vested in him had he become a member and contributor at the time his term of office began.

Any city officer who has not become a member of the retirement system but who was employed as an elected officer prior to January first of the year that the retirement system was established and who held such office at the time that the retirement system was established and has continuously held such office, shall be known as an original member and shall receive full credit for each year of service rendered by him prior to January first of the year the retirement system was established and for each year of service rendered by him thereafter, if such city officer shall contribute to the fund the amount which he would have contributed if he had become a member of the retirement system when it was established, in which event, the city shall contribute to his credit in the fund the amount it would have contributed if he had become a member of the retirement system when it was established, and he shall thereupon become entitled to all the rights and privileges in the retirement system as would have vested in him had he become a member and contributor at the time the retirement system was established.