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This all depends on the Judge or Jury. If this goes to trial, the judge or jury (by default the judge decides but the Defendant can request a jury) makes the decision on conviction. It is harder to convince a large number of people than one person, so most Defendants prefer a jury trial.
The onus is on the prosecutor to prove the case beyond a reasonable doubt.
What someone in your situation may wish to do is to subpoena the phone records (if they are available - text message records rarely are kept more than a few days by the phone company) to show that no message was sent from your phone, and/or, get witnesses to testify that around the time that the message was sent, you were doing something else and were not seen sending anything on your phone, for example.
So yes, it is possible to be convicted. But again, the onus is on the prosecutor to prove the case, so the Defendant has a natural advantage of simply denying the fact. The judge/jury decides in the end.
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