Upvote:9
This apparently refers to Allied Military Standing Order Nr. 153. While I couldn't find the actual text, the text The Execution of German Deserters by Surrendered German Troops Under Canadian Control in Amsterdam, May 1945 and a bunch of others mention it. Essentially, this order was meant to maintain discipline and order within the surrendered German troops. The easiest solution was to keep existing military structures intact until a better solution could be found. However, there were restrictions:
German military judges and commanders required written permission from Canadian corps district commanders for any sentence over two years imprisonment.
So in theory, death penalty had to be explicitly approved by the Allies.
Note that there are some discrepancies here. The text quoted above mentions that Order No. 153 was issued on 17 May 1945 by which time some deserters like Rainer Beck were already executed. According to the Spiegel Magazine article on Rainer Beck however Order No. 153 was already issued on 4 May 1945 and should have prevented the execution - but didn't because the people responsible claimed not being aware of it.
As to the person likely responsible for the order: the commander of the First Canadian Army at that time was Harry Crerar.