When her mother came, she pretended to be studying.

Literal

Mother [subject-が] came [when-とき], she [topic-は] studying-[ongoing-ている] pretense [object-を] did

~ふりをする = 'to pretend to do X.' ふり (振り) = manner/pretense. 勉強しているふり = 'the pretense of studying.' ~とき marks the temporal condition.