We all know that Google Search Appliance learns all the search queries that are getting executed and then it generates the Autosuggestion list.
However If you want to migrate all autosuggestions from one production box to another then there is no feature currently available to achieve this task.
There is a feature request # 4411407 for allowing import query suggestion into GSA box.
However I wanted to achieve this by some custom means So I followed the below steps and it worked perfectly fine.
1) Export the suggestion in text file from first GSA Box.
2) Write a script to read each line from that files and execute the search query against word /phrase to new GSA Box.
3) This will create a new autosuggestion list in new GSA Box.
Hope this Helps!!!