Normally, the Messages icon shouldn't be available for deletion. It's considered as being a System application therefore the delete button shouldn't work. However, if the phone permitted this operation, then you will have to take different steps:
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If it's a feature phone, it requires servicing from your local phone service or at the warranty service from your carrier.
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If it's Android, install another SMS application (GO SMS from Play Store)
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The iPhone or Windows phone devices don't allow this operation no matter you do.
