Chugalug
The worst problem is, that I have limited knowledge on cryptography and this part of history, despite having a 1920 Polish Bolshevik war code breaker in my family - never knew him, though. Everything I can gather on this is from books and few papers I have, and there are really few books.
I have found some more information, making the situation even more complex. It seems that the British who initially refused help to the Polish code breakers, then wanted them for Bletchley Park, but it turned out the French took the care of them, and did not allow them to go. Hence Bruno and then Cadix centres. As to messages from Cadix, they were send by radio with single use codes send from the UK. Such codes are hard to break but slow in use, contrary to machine codes. The actual role of France during WWII is quite mysterious. It seems that quite a number of high ranked persons of Vichy were pro-Allied, but they were overshadowed by the Free French, who were rather keen to take over any glory.
I do not know anything about German code breaking, but as far as I know, knowledge on German intelligence is quite limited. I do not know if documents were lost or taken over and still classified.
Best wishes
Franek