。
She is convinced of her son's success.
Literal
She [topic-は] son [genitive-の] success [object-を] is-being-certain-of.
確信する ('to be certain of, have confidence in, be convinced') takes the thing one is certain of with を. Built from 確 ('certain') + 信 ('belief'). The ~ている form indicates an ongoing certainty rather than a momentary becoming-certain. Note that 確信 carries a stronger 'I'm sure of this' note than 信じる ('believe') — the latter can leave room for doubt; 確信する largely doesn't.