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Yes. The sentence
Oн не знает, где билет потому, что его жена дала свой билет своeй подругe.
is about his wife's ticket.
However, the sentence has become clumsy because when we read "Oн не знает,...

If you understand that, then I would expect you to understand the third person as well because with your example it's exactly the same thing:
Я не знаю, где мой (not свой) билет.
Ты не знаешь, где...