Learn Russian: Этот фальшивый союзник оказался шпионом.

The verb оказаться (to turn out to be) requires the noun or adjective that follows it to be in the Instrumental case. This is a common rule for verbs that show a change of state, the manifestation of a state, or assuming a role (like turning out to be, remaining, or pretending to be something).

In English we say 'turned out TO BE a spy'. Why isn't the verb быть (to be) used in the Russian sentence?

This is a very common trap for English speakers! In Russian, verbs like оказаться (to turn out to be) and притворяться (to pretend to be) link directly to the noun in the Instrumental case. Adding быть (e.g., оказался быть) is a direct translation from English and sounds grammatically incorrect in Russian.

Could I use the word ложный instead of фальшивый for 'fake' in this context?

Not really. Фальшивый is used for things that are fake, forged, or counterfeit (like an imposter, fake money, or fake documents). Ложный translates closer to 'false' or 'untrue' in a logical sense, like a false alarm (ложная тревога) or a false statement. Since the ally is a deceptive imposter, фальшивый is the natural choice.

Оказался is the perfective past tense. What is its imperfective pair, and how would its usage differ?