If I text a broken iPhone will the messages show up if/when the phone is fixed?

My friends phone fell and broke. It's still in one piece but it's screen doesn't work and is all black. When I text it the messages don't go through but shortly after it broke I would text it without knowing. Will these messages show up on the phone is she's able to fix it (assuming she does)

Maybe, a text usually is avail for around 3 days, after that time the text will be gone forever.

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