。
She carried on his will.
Literal
She [topic-は] his [genitive-の] will [object-を] took-over.
意志 ('will, intention, volition') is the abstract psychological/spiritual sense — distinct from 遺言 ('will' as a legal document). 引き継ぐ ('to take over, inherit, carry on') is a 複合動詞 from 引く ('pull') + 継ぐ ('succeed to, carry on') — succession, inheritance, transmission. Used for businesses, traditions, posts, and abstract things like wills, missions, dreams.