yes the CORAL tongue can move

(y'all know I love ya). I think you should let it be and get where its gonna be happy
tongue corals are of the genus FUNGIA. they are found on reef slopes and flats between lagoons and the reef. they are usually on rubble or soft bottoms (dont even go there, heather and phishnoob, ha ha!) and like areas protected from strong wave motion. they should be placed such that they will not be damaged from a potential fall. they are easily damaged from handling. they should not be placed close to other corals as they deposit a thick mucus on other corals. feeding is recommended. (the book I am referencing, Aquarium Corals by Eric Borneman, does not specify what to feed, specifically). it says in the aquarium, fungia prefer low to moderate current and bright light. they are mostly nocturnal. they can move and tend to move toward light. they are capable of moving up to 12 inches per day and up a 30 degree slope. they are capable of righting themselves if flipped over, and can 'unbury' themselves from sand and easily rid their surfaces of debris. they may split in the aquarium producing daughter colonies.
I hope this is helpful

I needed to practice my typing (which is paraphrased, not verbatim, from the book mentioned above).