Will I receive an unlocked iPhone 5S if my locked iPhone 5S ever needs replac...
Apple's standard policy is to transfer the lock and warranty status to any replacement device. In fact it's automatic and based on the imei. So if your device is unlocked, then the replacement device will be unlocked. You can verify this with any worker at the apple store.
It doesn't matter if you got the unlock done via your carrier or a 3rd party or If it was a factory unlocked device. Those 3rd party sites get the unlock done the same way. It's all registered in apple's database. This is actually kind of a benefit of having an iPhone vs other gsm phones. Usually unlocking on gsm phones is device based, you have to enter the unlock code into the device. So if you changed device you'd have to pay to unlock the new one again. Apple has a database that's based on imei and there's no code involved. The only exception is they Gevey sim stuff.
There are lots of free sites to verify your unlock status but the best way is always to check with one of the apple store reps or itunes. If you do a restore on iTunes it will always give you the "congratulations, your phone is unlocked" screen for an unlocked phone. You can also do a check with your carrier over the phone.
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