。
She put in a good word for him.
Literal
She [topic-は] his [genitive-の] sake [for-ために] putting-in-a-good-word did.
口添えする ('put in a good word for, recommend') combines 口 ('mouth') + 添える ('add, attach') — literally 'add a (good) word.' Used when one person speaks up on another's behalf to a third party — for jobs, opportunities, marriage matches. Implies social capital being deployed for someone's benefit. ~のために marks the beneficiary.