Learn Polish: Podczas śledztwa okazało się, że polityk wymyślił tę historię. - During the investigation, it turned out that the politician made up this story.

When okazać się (to turn out) is used impersonally to say 'it turned out that...', it takes the neuter singular form in the past tense (okazało się). Because there is no specific noun acting as the subject, Polish defaults to this neuter form.

Why do we use tę historię instead of tą historię?

The verb wymyślił requires a direct object, so we use the accusative case. The strictly correct accusative form of the feminine pronoun ta (this) is tę. You will frequently hear native speakers say tą historię in casual speech, but tę is the grammatically correct form for writing.

Why does the word śledztwo change to śledztwa in this sentence?

The preposition podczas (during) always requires the noun that follows it to be in the genitive case. Since śledztwo (investigation) is a neuter noun, its genitive form takes an -a ending, making it śledztwa.

Could I use the imperfective verb wymyślał here instead of wymyślił?

You could, but it changes the meaning. The perfective verb wymyślił emphasizes the completed result: he successfully fabricated the whole story. If you used the imperfective wymyślał, it would mean he was in the process of making it up, or that he used to make up stories regularly.