From my experience, your credit does not follow you around the world.
When we moved to Australia it was as if we did not exist credit wise. That being said, they (companies etc..) were much easier to deal with. They relied on a more personal approach to granting credit (letter from employer verifying income, copy of your lease etc...) In fact, we had only been in the country for a couple of weeks, walked into a Toyota dealership and purchased a new car, obtained a loan for AUD $80,000 without a hitch. I found that once we obatined a drivers license in the country--it was easy to come by credit. By the way, once we paid off the car, Toyota wrote a nice letter thanking us for paying on time for the duration of the loan --they did this without any prompting!
Now, my hubby lives in Hong Kong right now, he got credit there based on his banking relationship with HSBC in Hong Kong. Also, as a Premiere customer there he apparently is entitled to having his "credit record" from Hong Kong shared with HSBC in the US or anywhere else in the world if he wanted to. So, if you open an HSBC account here in the US you can have your "credit" shared with HSBC in any of the locales they service (I don't know if Russia is one of them)
As for American Express, all we had to do was contact AMEX in Australia and they sent us a form asking all of the info on our US account and boom we got an Australian Amex. Did the same thing in Hong Kong.
You really need a credit card in the currency of the country you are living in. We found that there were cases where you needed (for example) an Aussie card for some purchases. Also, some US credit card companies have a tough time with foreign addresses. Additionally, you don't want to have to deal with currency exchange rates.
I would suggest, you really have a plan in place to manage all of your financial affairs for the US if you have any outstanding debts, mortgages etc...With time differences, the cost of wire transfers, and the sheer hassle of maintaining two financial lives it is really important to keep up on things.
One more thing I have learned, with the exception of HSBC (Premiere accounts only) you will be charged to transfer money between your own accounts with the same institution. For example, if you have a B of A account in Hong Kong and you want to transfer money to your B of A account in the US --it is as if you are banking with unrelated companies. You cannot just simply transfer funds--they must go through the wire process and you will be charged (sometimes in the neighborhood of $45) Plus, you pay the charge on both sides (making the wire and receiving) If you have substantial funds in the US that you rely on your ATM card will become your new bestfriend.
If you want any more questions asked--just ask away--I have been living like this for quite a while and know many of the ins and outs!
Cheers!