Banks are required to have certain documentation on file concerning their customers.
Yes, she should complete the form if the bank is asking
W-8BEN is just for the bank's records. It would not be worrisome to fill it out. It does not get forwarded to the IRS or anywhere outside of the bank.
Form W08BEN lets the bank know how much, (if any), tax they need to withhold on your income, (if you have any income), such as interest earned.
The bank will probably not need to withhold tax, but they are required to have some sort of documentation on file that they inquired about your tax status. If they were to withhold tax, that would all be reconciled on your tax return.
Since you file Form 1040 as a resident for tax filing purposes, Form W-9 might be more appropriate (in my eyes) but regardless, either form does the same thing. Since it's a foreign bank, they might not have Form W-9 and only use Form W-8BEN.
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