Short answer
CBP can search information that is on the phone when it’s presented for inspection. Under CBP policy, officers may not use the device to access information stored solely remotely in the cloud. Before a basic or advanced search, they must disable data and network connections. Officers may do this by asking you to use airplane mode and disable Bluetooth and Wi Fi, or by disabling connectivity themselves. Information already stored on the phone can still be examined.
Useful official link: CBP, Border Search of Electronic Devices at Ports of Entry
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