Yes that a SB red dragon and that's all you really need to do, besides keeping water clean and good parameters, he should heal up fine. That said I'd also ask if his new tank is already cycled? If not grab a bit of bio-media (or sponge filter, decorations) from your established tank asap.
Afterwards if you really want to see his best then keep him (and the other FH) solo is always my personal recommendation.