Tell me how would they do it?
Obviously you know!
The same ways and means used to get other information that it's holders do not want them to have. Not just one technique, many techniques. Sometimes poorly applied, they are government agencies. They'd probably hire a contractor for the actual work, but maybe not.
One potential means, they could hack into the Hawaii DoH computers. Why not, the Chinese and Russians probably already have. Even more likely the Israelis, who also would have good survival reasons to want to know, and to leak what they know.
One low tech, but effective, method that I've been briefed on more times than I can count, is the "honey trap". Some lonely, and possibly not too attractive, lady in the Hawaii DoH gets wined and dined and generally paid attention to, maybe laid as well. It can be tough work, but the Soviets had it down to a near Science. She wants to please her new "friend", so thinking "what could it hurt" supplies him with the goods. Then he disappears, but not instantly. She might not even connect his "breaking it off" with her supplying the data.
It's happened before, it'll likely happen again.