Lost iPhone

If the battery is dead, there's no other Apple service that can find, track, or flag your device for you.

You can still follow some of the steps (to help protect your data) in:

If your iPhone, iPad, or iPod touch is lost or stolen - Apple Support

in case someone finds the iPhone and chargers the battery.

If it's in your or his house, physically search for it. If not, post notices around where he lost it, or contact the police, or if applicable, the Lost and Found department of the facility where he lost it.

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Then it’s likely gone.

If your iPhone, iPad, or iPod touch is lost or stolen - Apple Support