My friend is a Russian citizen who once worked in the US but now lives in Russia.
How can she get her money from her US bank account?
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She may ask the US bank to issue a debit card (VISA most probably) to her account, and mail this card to Russia. I think this can be done without much problems, though sending anything by mail may be unreliable. After this she just withdraws the money from local ATM. Some withdrawal fee may apply, which may be rather big if the sum of money is big. In big banks (Alfa-bank, Citibank Russia, etc.) are ATMs that allow you to withdraw dollars, and it is better to use one of them to avoid unfavorable exchange rate.
She may ask the US bank to transfer the money to her Russian account. I assume the currency on the US bank account is US Dollars. She needs an US dollar account in any Russian bank (this is no problem at all). She should find out from that bank the transfer parameters (реквизиты) for transfering US dollars to her account. This should include, among other info, a "Bank correspondent", and a SWIFT code (or may be two SWIFT codes).
After this, she should contact her US bank and find out how can she request the money to be transferred to her Russian bank, providing these transfer parameters. I can think of two problems that may be here. First, the bank may refuse to transfer money without her herself coming to the bank to confirm her identity. (How do they know that a person writing or calling them is she indeed?) However, I guess there should be some workaround for this. Second, with current US sanctions against Russia, the bank may just refuse the transfer or will have do some additional investigations. However, I have heard that bank transfers from US to private persons to Russia are not blocked. Probably it is good to find this out in advance. In addition, the US bank will most probably charge some standard fee for foreign transfer.
After this, she should wait for a couple of days, maybe up to week for the money to appear on Russian account.
I have done this once some four years ago, and had no problems, though at that time I was in the US, so I just came to the bank myself. The bank employee to whom I talked obviously was unsure whether the transfer parameters were enough (obviously this was a very unusual situation for her), but she took the information from me, and I guess just passed it on to someone more knowledgable. The fee was something about $40.
Another option that I might think of is her US bank issuing and mailing her a check for the whole sum, and she trying to cash it here in Russia. This is possible, but very few banks do cash checks here (Citibank Russia is among those that do). The bank will also charge a fee, and it will be comparable to transfer fee. Plus mailing anything is not quite reliable here.
UPD: As of 2020, Citibank Russia apparently no longer accepts checks, and I don't know of any other bank that does.
She would also have to consider whether she need to pay Russian taxes on this sum. If the sum is big and passes through a bank, I guess Russian tax police may find this out through and question her. If it is withdrawn from a VISA card, I think it will not be noticed, but even in this case she might be required to file a tax herself.