Sorry that I'm rather late in replying to this.
The process for finding an actual grave in Russia is not that different from finding the location of a grave in the UK (you really need to contact the specific cemeteries directly as they are the people who will have records of who is buried where in their cemetery).
It's great that you know where and when he died. What you will need to do is to contact the local cemeteries and/or the local Registry Office where your relative died, or have somebody local contact them on your behalf.
So, for example, one of my siblings parents-in-law are of Russian descent. They come from a city of about 400k people (so, about the size of Bristol) about 100 miles north of Moscow. There are eight cemeteries in that city.
You would either need to approach the local Russian equivalent of the Registry Office (called ЗАГС [ZAGS] - отдeл записей актов гражданского состояния or dept of civil registration acts) who record all the births, marriages and deaths. Or, alternatively, approach the individual cemeteries.
To be frank, unless your friends can speak Russian to a near-native level (and also understand the Russian system of recording births, marriages and deaths) then you are likely going to have real problems doing this yourself.
Even Russians have trouble finding the location of Russian graves (just as much as it can be difficult to locate an actual grave in this country). So there are local companies that provide services to locate graves.
Whether you are better off going through a Russian speaking historian/genealogist based in the UK (as suggested above) or approaching a local Russian company directly, I really don't know.
But if you are searching for a Russian company to do the search for you then you need to use Yandex rather than Google (Yandex is the Russian version of Google) If you type in Yandex.ru it sends you to its Russian search engine called "dzen.ru" but if you type Yandex.com then it sends you to its non-Russian search engine which won't be of any help really.
Once you're in the Russian search engine then if you type in something like
Поиск могил в [name of city or region in Russian] - Search for grave in ...
or
Поиск места захоронения в [name of city or region in Russian] - Search for place of burial in ...
Either of these searches should give you some local companies in that area that do this sort of work on behalf of Russians.