Is it possible for iMessage to do this?

If your phone is off but you can still use iMessage to text other iPhones because you have Wi-Fi do the other person who phone is on have to use Wi-Fi to receive the iMessage u sent them and the ones there trying to send to you. Or since their phone is on they don't need Wi-Fi to receive iMessages or send then

As long as you have Wi-Fi they will be able to send you iMessages. They do not need Wi-Fi to do this

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