Only if they are clones - genetically identical. So not much use in practice, unfortunately.
I think the article says they just haven't tested other cases. I wouldn't expect the symbiotic microalgae to be that picky.
Edit - The article makes Okkef's point, I just missed it.
Sounds like a solution is still well within our reach. Normally I wouldn’t suggest something as extreme as using cloning techniques to restore wild creatures, but of course it was extreme actions that got us here in the first place, so I think this balances it out.
We could create a bank of coral clones tagged to each individual location.
High temperatures affect the algae itself. Transferring the algae to another live coral (bleached coral is alive) a) already happens in nature, if conditions return to normal b) does not protect the algae