I have found a statement on one of Russian sites:
They (photographs) often shoot in RAW, and it, in turn, removes various small spots in the form of dust on the lens when converting.
Is it true? If yes, how to do this (what converter does this)?
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That statement from the Russian site is misleading. Shooting in raw format doesn't have any relevance to spot removal. You can remove dust spots just as easily with any other format of image.
There are multiple ways of clearing dust spots:
Basically it's just a cloning/healing procedure. But the best fix for dust spots is to clean your sensor.
Lightroom can do that. I am sure other applications have similar features. Here is a tutorial how to do that. Also please note that, as written in the linked article, you will have to go and check on the result yourself and improve on it. It is not 100% foolproof.
Some camera's have dust removal built into the JPEG conversion engine. They map the found dust on the sensor, and digitally remove it in the JPEG conversion. I don't know of a camera that preserves this information in a RAW file, but if it did, it would require specialized software to read and convert such information.
RAW by itself does not remove dust digitally.