Interesting question! This is specific enough that I'll keep it here for now, but I might link to it in future if other people ask.

His phone would display whatever time it was just before he woke up here on the beach. It will seem to keep time "correctly" in relationship to the original displayed time for as long as it has battery life, but if it's ever switched off and on again, he'll notice pretty quickly that it isn't keeping track of time while the battery isn't running.