Personally I would say never, unless it starts to melt or turn white. Corals can take days, or weeks, or even months to fully acclimate to a new tank, depends how different your parameters are compared to where it came from. Every time you move it, it has to start readjusting all over again.
What is that coral, it looks like a leather coral, perhaps a toadstool? Leathers normally like medium flow and medium light (if its a leather).....