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Hello! Yes the signs are in Russian and English under them. In immigration, it's difficult to say because  it depends on the foreigners and immigration officers. But usually, it's not very long. With baggage claim, yes that one is the longest...I can tell you, I would always spend my 20-40mins there Have a nice day!

Hi.
Both Airports have signs in multi languages(ru/en).
Passport control is always unpredictable, and sometimes very chaotic.
In my worst experience, I had to stand on the que for 1 hour.

Transportation between Vnukovo and Domodedovo is also unpredictable(if you choose car).
I know many friends who missed their flight due to heavy traffic.
Better to check on maps like Yandex or Google which will roughly tell you approximate time.
It can be an hour, sometimes 4 hours.


If you would like to stop by in city center(like Kremlin), you should have extra hours.
Maybe it'll be a good idea to take Aeroexpress and Metro between the Airports.

They are usually very punctual.

I suggest you to use Vnukovo airport, the authorities at the Domodedovo airport are horrible nowadays.