'Be through' in this context means 'have finished', so it can't be followed by an infinitive or conjugated verb. The correct answer is 'rehearsing'.
However, this use of 'be through', although understood, is not really natural in BrE.
You could make a case for 'to rehearse' being the right answer, if you take 'be through' to mean 'come into the place where the rehearsal is taking place'.
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