Transfering records with foreign key referring to new value
There could be few approaches you can take to achieve this... based onhow big is the data set.


Use of cursors
Using cursor you can insert each row is new warning table capture the new_warningid created for that row and use it to insert respective Acknowledges referring to old_warning id and replacing with new_warningid.
use of temporary column in New_warning table which will hold old_warningid for lookup.
Add a column "old_warningid" to new_warnings table and use that column as lookup while inserting rows in new_acknowldges tables to get corresponding "new_warningid".once the migration is complete you can drop the columns from new_warnings table.