Am I correct that the "imported unique identifier" is NOT the same value used in your two tables in their match fields?
If so, create a new table occurrence of at least one of the two tables. Make sure that you have fields in both tables for this imported id. Link the new occurrence to either a new occurrence of the second table or the existing occurrence by the imported ID fields.
After Import, Use this new relationship and Replace field contents (this can be scripted) to update the match fields of your original relationship.