Awk merging of two files on id

Awk merging of two files on id

I would like to obtain the match the IDs of the first file to the IDs of
the second file, so i get, for example, Thijs Al,NED19800616,39. I know
this should be possible with AWK, but I'm not really good at it.
file1 (few entries)
NED19800616,Thijs Al
BEL19951212,Nicolas Cleppe
BEL19950419,Ben Boes
FRA19900221,Arnaud Jouffroy
...
file2 (many entries)
38,FRA19920611
39,NED19800616
40,BEL19931210
41,NED19751211
...