The correct term is "investigation of".

to ensure that the investigation meets the objectives of the investigation if the process in investigation were done properly and the end result of the investigation of the case is effective and efficient or a case is already filed in courts

a valid investigation is an effective investigation i think. The results turn out to be what you had inferred.

Repetition is copying an investigation, while replication of an investigation is the results of an investigation, which is not likely to be accepted unless the investigation is repeated multiple times and the same result is obtained.

A good tip for software purchasing, it to do your research before making the purchase. There are many software review sites that list user reviews, where you can conduct a thorough investigation.