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Presumably this is why she doesn't have to pay:
IRS: foreign earned income
Foreign-earned income of up to US$80,000 is exempt if you live abroad.
Seems bizarre to me that otherwise (and above that) you have to pay.
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there are three different ways to get foreign income out from under US taxes to a limited degree. which is most advantageous depends on your income, other deductions etc etc.:
section 911(a)(1) foreign income exclusion. up to $80,000
of your income, with tests for residence or presence abroad.
section 27 foreign tax credit. (not in my statutory supplement.)
section 164(a)(3) "state and local, and foreign, income, war profits, and excess profits taxes." this is just a regular itemized deduction. it tends to be the least advantageous.