The FBI didn't disclose the identity of the third-party company that helped them access the San Bernardino iPhone, but it has been widely believed that the Israeli mobile forensic firm Cellebrite was hired by the FBI to put an end to the Apple vs. FBI case.
For those unfamiliar in the Apple vs. FBI case: Apple was engaged in a legal battle with the Department of Justice over a court order that was forcing the company to write software, which could disable passcode protection on terrorist's iPhone, helping them access data on it.
However, Apple refused to comply with the court order, so the FBI hired an unknown third-party firm, most likely Cellebrite, who managed to successfully hack the locked iPhone 5C used by the terrorist in the San Bernardino shooting incident last year.
The new method helped the Federal Bureau of Investigation (FBI) to hack iPhone 5C, but that wasn't the FBI's victory as the method didn't work on iPhone 5S and later iPhone models.