"She does not find her purse."
Translation:היא לא מוצאת את הארנק שלה.
It's always a little irksome when Duo (at least seemingly) throws a random new term at us without introducing or explaining it. So, as you say, it replaces לא rather than meaning "doesn't have" ... because I would have guessed that saying " היא) איננה הארנק שלה) " would mean "she doesn't have her wallet/purse"
This is another example of the different English/ American uses of words. In British English a "purse" is the thing with coins etc - equivalent to a wallet though purists might say that a purse only holds coins, not notes while a wallet holds notes and sometimes also coins. A bigger receptacle is called a bag or handbag.
Thanks! This saved me the trouble of asking whether Israelis distinguish between wallets and purses!
So an ארנק is the holder of cash and cards that goes in your pocket, that Americans call a wallet, and that Brits call a wallet/purse, while a תיק is a larger container with a strap, mostly used by women, that Americans call a purse/handbag/bag and Brits call a handbag/bag. Is that right? (FWIW, the word "changepurse" exists in American English, meaning something that only holds coins, but both the object and the word are rare.)