Conversation so far:
When did Josef Mengele join the military?
Mengele joined the Nazi Party in 1937 and the Schutzstaffel (SS; protection squadron) in 1938.
What was his rank?
he served with the rank of SS-Untersturmfuhrer (second lieutenant) in a medical reserve battalion until November 1940.

Question: What did he do after 1940?
Self-contained rewrite: What did Josef Mengele do after 1940?