She passed the gem off as her own.

Literal

She [topic-は] that gem [object-を] own [genitive-の] thing [as-として] pushed-through.

通す ('to make pass, push through') in this idiomatic usage means 'to maintain a claim or stance through to acceptance' — to get something believed or accepted as fact. Combined with ~として ('as'), the structure ~ものとして通す means 'pass off as / claim as.' The verb has a willful, almost stubborn flavor — you 'push through' a story, an opinion, a lie. 自分のもの ('one's own thing') is the natural Japanese for 'one's own property.' Together, the phrase implies deliberate deception sustained until accepted as truth.