"The Big Bad Bug Syndrome" is the fifth episode of Season Two, and the 18th overrall. it originally aired on October 24, 1998. It was written by Greg Weisman and directed by Christopher Dozois. The Queen of the Bugs puts out a bounty on the MiB agent responsible for the demise of dearly-departed...
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This is sufficient evidence that the series is a sequel to the first film. There's a flashback to the first film but in animated form, Vincent D'Onofrio reprises his role and plays relatives of his character.
The only evidence otherwise, that being the in-universe film, I have disproven. To quote someone I know who has actually seen the series, "I know there was meta joke with a film but it was so different than what happened in-universe that I didn't feel like mentioning it".
If the in-universe film is clearly not the same as the film we've seen in real life, and the events of that film are shown to literally happen in the reality of the series, it stands to reason that they're the same universe. Further, there's a comic set after the first film where K gets de-neuralyzed, which fits perfectly between the film and series.
It's also not a stretch that K could get neuralyzed again either.
