Yes, your mother can get credit for Foreign Tax she paid on her US income, and you are correct that she will not be double-taxed on this income.
When she reports her income in TurboTax, the Foreign Tax Credit is in lieu of US tax that would be assessed on her US income.
Here's how to claim the Foreign Tax Credit:
https://ttlc.intuit.com/replies/3302405
Click the link for a more detailed article on Form 1116, Foreign Tax Credit.
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