As an example, when Germany conquered France, were there roving bands of German military personnel knocking on the doors of the French intelligence services, the military and defence companies? How was this carried out in practice? Was there much review of the the archives of the French military and its intelligence agencies? To what extent were these secrets destroyed before the Germans could get them? I would be interested in any country Germany invaded.
When the Allies captured Germany, and when Japan surrendered to the US, what was the process whereby German and Japanese secrets were plundered? To what extent were their discoveries shared between the Allies?
I am somewhat familiar with Operation Paperclip, so for the Allies' portion of this question, I am more curious about non-missile/rocketry secrets that were plundered.
There was no big process for the Germans - they learned most from captured units. For the French, many strategies and units were known before the war - Abwerh did a good job, while captured units played a larger role in Russia and UK - they studied it. In UK, air recon was also effective, while Abwerh didn't have experienced enough units to send then to UK. USSR managed to destroy most of the documents, and even air recon was misleading, so all they learned from USSR was by captured troops and technicals - the Germans laughed in amusement when they saw the BM-13 Katyusha Rocket SPG's, but later realized what they could do and followed up with the Nebelwerfer. About the T-34 and KV-1 they learne the hard way - in battle, where they killed their Panzer III and Panzer IV tanks. The strategy was known before the war however, and here german recon was effective.
Well, without Operation Paperclip, there was no big operations done. The Allies found the secrets and documents simply by taking the positions there. Like, the German flyinh wing - Ho 229 - was simply found in a hangar, which was taken with a German village nearby. The same was with the mountain complex the Me 262 was made. But these secrets were one of the main reasons Allies were rushing to take German land - so that the Soviets gained lese German technology.
About Japan, there were no big chases as well - some (like the Japanese POW camps) were conquered, others were shown after the war ended. Others, like the Iwo Jima tunnel system (if you call that a secret), were nevef explored to complexity, making clashes with lone Japanese squads even after war was over (the last surrendered in 1950).
If you do not count the Soviets in the "Allies" block, these secrets were well shared by the West, for example, the mentioned Ho 229 were sent to the US after the British examined it. And they weren't hesitant to send the information further in the Commonwealth. It was beneficial for all members of the block, as they could faster study the block.
EDIT: There were some mistakes, and I hope I could help you. Well, this seems to be my baptism of fire for reddit.