Could you explain to me the meaning of "amid claims".
Read amid as "in the midst of" or "in the middle of". Or basically, "at the same time as something else is going on".
German prosecutors are re-examining the 1919 murder of the communist leader Rosa Luxemburg, amid claims investigators at the time replaced her corpse with that of another woman.
- "German prosecutors are (currently) re-examining the 1919 murder of the communist leader Rosa Luxemburg, in the middle of a (period of) time that people are claiming that (other) investigators (in 1919) replaced her corpse with that of another woman."
So the new investigators likely didn't come out and make a statement that they were re-opening the case because they thought a body was swapped. It's just something that non-official sources were saying. Then, during that same time--or "amid (the period of time that) claims (were being made)"--an investigation was opened.
Whether this gives particular support to body-swapping in particular, the writer would probably go on to say. But it does give support to the idea that previous official accounts are suspected of some inaccuracy.