(1) Alex had quit his job and started a company before he won the lottery.
(2) Alex had quit his job and had started a company before he won the lottery.
I want to indicate that the act of quitting the job and starting a company happened before winning the lottery. I think (1) is grammatically correct and conveys the intended meaning. The word "had" before the word "started" in (2) seems unnecessary. Is my understanding correct?