FAA: Light Sport Time Can Go Toward Private Cert. (Sometimes)
So, can a student pilot apply any flight time he or she logged while training for a sport pilot certificate toward a private pilot certificate? According to a letter from the FAA's Office of the Chief Counsel to aviation journalist Tim Kern, who queried the office, solo sport pilot flight time may only be credited to solo private pilot flight time if the "specific category and class of aircraft are met." Logging instruction time depends on the instructor's credentials. If instruction is received from an instructor who holds only a a sport pilot rating, that instruction may not be credited toward the issuance of a private pilot certificate. However, if the instruction toward a sport pilot certificate is provided by an instructor authorized to provide instruction to both sport pilots and private pilots, that time could "be credited toward the flight training requirements for a corresponding private pilot certificate." There are more details ... .
According to the letter, "flight time obtained in a certificated aircraft prior to the issuance of a private pilot certificate, regardless of whether that flight time was obtained prior to, or after, the issuance of a sport pilot certificate may be credited toward the flight time requirements for the issuance of the private pilot certificate." Kern has posted the full text of the letter here (PDF). It explains in detail that a sport pilot instructor (SPI) is not qualified to give dual for a private certificate and therefore any instruction given by an SPI is not applicable toward the private.