I have worked on a number of 32's,K 32's,and K 80's. Two weeks ago it was a very early K 32 with a K type of trigger, but a frame of a 32. The serial # less than 200.In two other cases the guns were early K's with 32 internals. The K people said "good luck on finding parts".I think that the transition to Germany involved the DuPoints(as I have been told) and the guns have evolved internally over the years ( including several versions of the K 80).Being "told" is perhaps not the actual fact. That includes the "told" that Miller of the trigger family was not happy with the newer trigger system. A very detailed article of how to convert a 32 to K is to be found in "American Gunsmith" Volume XIX Number 11 November 2004. Good luck on buying all of the parts as the factory will not part with the sears.
