Any firefighter who has become an employee of the first public agency because of the assumption by that public agency of the firefighting function of the second public agency who, at any time after becoming an employee of the first public agency, pays into the retirement fund of that first public agency the same amount which he or she would have contributed had he or she been employed by the first public agency at the same salary, and for the same time or periods of time for which and during which he or she was employed by the second public agency whose firefighting function is assumed by the first public agency shall have all of the retirement rights which he or she would have had, if any, had he or she been an employee of the first public agency at that salary and for the time or periods of time, unless the first public agency has provided by ordinance pursuant to Section 45310.5 for a modification of his or her rights and benefits because of membership in a reciprocal retirement system.