WELLINGTON, New Zealand — Revelations that a New Zealand lawmaker had been a member of the Communist Party in China and taught English to spies there have raised alarms about Beijing’s influence in New Zealand — and how well the political parties there vet their candidates.

Jian Yang, a lawmaker with the center-right National Party, did not declare his past Communist Party affiliation or his work teaching spies in China on his New Zealand citizenship application. He was returned to Parliament for a third term in the country’s Sept. 23 elections.

Days before the election, as some New Zealanders were casting advance ballots, Mr. Yang’s background was exposed in a joint investigation by The Financial Times and the New Zealand online media outlet Newsroom.

While New Zealand is a small country, it is a member of the “Five Eyes” intelligence sharing partnership along with the United States, Britain, Canada and Australia. And so vulnerabilities in New Zealand’s government could have wider import.