If the phone has taken on moisture while it is turned on it will most of the time short out and go into recovery mode. Sometimes if one can act very quickly to turn it off, not connect to power, and let it dry they might be turn it on later and get a backup done prior to taking it in. I know of very few phones that were exposed to water that were turned off at that time. The best thing to do is automatic iCloud backups.
Make an appointment at the Apple Genius Bar for service. If you need to find an Apple Store - Find a Store - Apple. Do this ASAP.
"Make an appointment at the Apple Genius Bar for service. "
This is a good advice as long as the appointments is within few minutes/two hours. In other cases the phone is being eaten by corrosion while the customer is waiting for his turn. I would appreciate if Apple had triage as hospitals do. In case of water damage time is of essence if the goal is to save the device.
If you have put a 3rd party screen on your iPhone do not be surprised when Apple tells you that they cannot help you. Depending on the model iPhone you are referring to then you probably do need a logic board that will be almost impossible to find. Your only option will probably to find a reputable 3rd party repair shop that can work on water damaged iPhones.
Since Apple replaces the iPhone in cases like this and does not repair them their is no triage need. The battery is not user accessible so your advice to remove the battery does not apply to 99% of the incidents that occur and in most cases the phone will have already gone into recovery mode so all the data they had not backed up is gone.
AASPs do not do the water recovery methods you describe. At least they don't if they want to stay an AASP.
So what is the point to go there? If the phone is switched off it will not go to recovery, in that case the data would not be damaged? Or am I wrong here?
Dropped my phone in water help black screen
