Short answer is no. There is no copy of a log book. The cage number is usually on the passenger side of the main hoop. If you find the number the region number is the first 2 digits in the stamp and they might have a list to re-issue from. Best bet is to just have a new book issued. It will have to meet all current safety standards, and the cage changes over the years would be your only issue. Either way I would contact the chief of tech for your region.