Any contributor who resigns his or her position to accept and who, within sixty days thereafter, does accept another position in the city-service shall continue to be a contributor while in such city-service and shall be known as a transferred-contributor provided he or she executes and files with the retirement board a statement in writing that he or she elects to leave with the annuity savings fund his or her accumulated deductions and to continue to contribute to such fund at a rate of salary deduction not less than the rate of deduction theretofore required from his or her salary, and further provided that he or she shall waive and renounce any present or prospective benefit from any other retirement system or association supported wholly or in part by the city. Where an election is made pursuant to the provisions of this section, the salary deductions required by such provisions shall be appropriately modified, if a rate of deduction is otherwise fixed, pursuant to section 13-546 of this chapter, for the transferred-contributor making such election.