You can try it, but it may or may not actually work. If it is a healthy star, in a suitable tank, then they should be able to recover on their own. But most are severely stressed, and not in an ideal tank, which is why most are doomed.
Acclimation shock tends to happen within a month of introduction, and it is quite possibly what is happening here. I agree the acclimation time and specific gravity are far too low. In addition, if this is not a mature reef tank that is good sized (eg at least 75g with 125lbs of LR) then I would say long term success would be pretty poor for this type of Linckia.