Really, this is indeed the first and pretty show-stopping mystery. Immigration would simply not have allowed OP to exit immigration and just walk on to the next flight. They would have held him+family in the secure Immigration area while the crew searched the plane... it would have been a pretty easy search.

There is no way immigration officers will allow anybody to get past (can you imagine the consequences if people just started being let through on a verbal that they "lost" their passports on the way)?

I doubt if OP has a second set per the final comment " we are deep in the S we cant move further, no Passports."

Unfortunately without confirmation on how OP was able to make it past immigration and customs in FRA, the entire scenario does not add up. Sorry to be skeptical but really either I am missing something extremely obvious or there are huge holes in this impossible story.