Actually, there exist no 'rules' to govern whether a word is hyphenated or written as a single word. The most sensible guideline to follow would probably be to go with frequency. That is, go with what is the most common, which in this case is probably handheld, but it's really a question of style. This is often something that changes over time.
That's exactly my thought. But in this quiz that the author prepared, he says sentence 1 is wrong and sentence 2 is right. That completely contradict what he taught in his course material (and all other tutorials out on the web). As I remember, the author says, if in doubt use a dictionary, so I did exactly that. The dictionary notes a closed version of handheld.
To be fair, according to grammar rules neither is wrong; they are both grammatically correct because handheld exist in the dictionary and hand-held satisfied the compound adjective.
Then I wondered is there a precedence over which one to use?
I think the author should not have used the two sentences to illustrate correct grammar, because technically he is also wrong.