。
She was convinced that he was honest.
Literal
She [topic-は] he [subject-が] honest [is-である] [quotative-と] was-convinced.
~である is the formal/written copula, often appearing inside complement clauses where the spoken だ would feel too casual. 納得する ('be convinced, accept') takes と for the content of conviction. Compare 信じる, which leans toward 'believe (without evidence)'; 納得する emphasizes being persuaded by reasoning.