Copy Data from Two different databases with FK relation
This could probably be done with some ETL tool but
A manual way comes to mind:
 - just join the test tables together ( I'm guessing the join condition would be STEP_RESULT.UUT_RESULT = UUT_RESULT.ID) to get all the relevant keys.

SELECT a.ID 
FROM STEP_RESULT a join UUT_RESULT b 
on a.UUT_RESULT = b.ID


So lets say you get a 1000 values of b.ID. Then manually create a select which will have all the values returned from the TEST sql in an IN condition and run it on PROD:

SELECT * FROM PROP_RESULT WHERE STEP_RESULT IN ('ID1','ID2', ...)


Not sure how exporting data in MSSQL works but I'm guessing you could just save that select as a separate table and then just load it into your TEST environment