No... they won't.
Also, your friend should get both visas before leaving.
I gave exactly this advice to some business associates of mine before coming to the UK. They ignored my advice, and tried to get Schengen visas once in London - first of all from the French embassy and then from the German embassy. They were refused on the grounds that they were not resident in the UK and should have applied before leaving their home country. They got the impression that their might be some latitude from the German embassy in some circumstances.
They thought it would be easier in London on the grounds that once you're in the UK (a relatively difficult country to get into), getting a Schengen visa would be relatively easy compared with their home country of Vietnam.
YMMV