Primary Test: It will be rather rare to find flux melt red spinels of any size due to the high stress crystals created by this process. Inclusions will be the primary identification method as these stones tend to show characteristic inclusions as seen below. This includes a high probability for platinum platelet inclusions from the platinum crucible used to grow the crystals.
Secondary Tests: Spectroscope will be helpful as the amount of chromium used in the lab growing process imparts very strong Cr lines in the red portion of the spectrum. Due to the high Cr content the absorption lines are far more intense than would be normally expected in a natural red spinel. This should be considered a secondary test only.
Repair and Setting: Based on this being a true synthetic spinel no special care is required other than would be used with a natural spinel. Not recommended for torch heating, but cleaning in ultrasonic should not be a problem.