A friend is planning to make a trans-mongolian trip (Beijing - Moscow through Mongolia). The Russia and Mongolia visas are mandatory for this trip, but is it possible to travel through China using the 72-hour transit visa granted in the Beijing airport? Of course, the time in China will be less than 72 hours.
No, this is not possible. When using the 72-hour transit without visa at Beijing airport you are not allowed to leave Beijing and need to leave the city on a flight. Quoting the Chinese embassy in Canada:
A foreign national obtaining the 72-hour transit visa exemption at the airports of Beijing, Shanghai or Chengdu may not leave the administrative precincts of Beijing, Shanghai or Chengdu. [...]
A foreign national with the 72-hour transit visa exemption is not allowed to leave the city where the stopover is permitted. Therefore, a foreign national obtaining the 72-hour transit visa exemption at the Capital Airport of Beijing shall leave China from the same airport in Beijing within the permitted time of stay and may not leave China from the airport in Shanghai, Guangzhou or Chengdu. [...]
This measure is currently available only at the airports of Beijing, Shanghai, Guangzhou or Chengdu, which means the 72-hour transit visa exemption in Beijing is only applicable to a passenger obtaining it at the Beijing Capital Airport.
(The site – as any official Chinese site I know of – is out of date as the program has expanded to significantly more airports. The basic facts still stand.)
This is also evidenced by the current Timatic entry (emphasis mine):
Nationals of [many countries] holding confirmed onward airline tickets to a third country, if arriving in and departing from the same city:
at Beijing (PEK), Chengdu (CTU), Chongqing (CKG), Dalian (DLC), Guangzhou (CAN), Qingdao (TAO), Tianjin (TSN), Wuhan (WUH), Xi'an (XIY) or Xiamen (XMN) for a max. transit time of 72 hours, starting from 00:01 on the day following the day of entry.
at Guilin (KWL), Harbin (HRB), Kunming (KMG), or Shenyang (SHE) for a max. transit time of 72 hours;
A FlyerTalk Thread Wiki entry has the best and most up-to-date treatment on the exact rules of that program I know of. It also clearly states
The TWOV rules apply to air travel only at this time