Learn Portuguese (Portugal): Supostamente, a ex-mulher falou secretamente com o advogado. - Supposedly, the ex-wife spoke secretly with the lawyer.

You could, but it shifts the meaning slightly. Supostamente means 'supposedly' (based on rumors), whereas que eu saiba means 'as far as I know'. If you make this swap, the sentence becomes: Que eu saiba, a ex-mulher falou secretamente com o advogado. The main verb falou stays in the indicative because the subjunctive is locked inside the que eu saiba formula.

Why does ex-mulher require a hyphen?

In Portuguese, the prefix ex- indicating a former status always takes a hyphen before the noun it modifies, regardless of whether the noun starts with a vowel or consonant. You will see this consistently in words like ex-marido and ex-presidente.

Why is the adverb secretamente placed right after the verb instead of at the end of the sentence?

Adverbs of manner, especially those ending in -mente, generally sit immediately after the verb they modify (falou secretamente). Putting it at the very end (falou com o advogado secretamente) is grammatically possible but sounds much less natural to a native Portuguese ear.

Why use the preterite past tense falou rather than the imperfect falava?