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...if Sherlock had come back with Moriarty and his network gone...but his own name not completely cleared? And that had been something he still had to accomplish through the episodes?
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I think they deliberately let that happen off screen because they wanted to get on with the story. They already squeezed quite a lot of story in 90 minutes. The name clearing would have to replace the terrorist plot or the character work. But if you see a way in which it works, why don't you write it? Your alternative version of TEH, see what will happen. It might be very good.
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Pretty easy to clear his name. The obvious cases like Ricoletti who had been most wanted since Sherlock was a child. (A major case the Chief Inspector seems to have forgotten about when he says 'not used him on any proper cases, have we?') The Hound which was an old case as well.
And all the Moriarty linked cases that MI6 would have known the truth about.
I suspect that once Mycroft decided to bring Sherlock back information clearing Sherlock would have been leaked to the police, etc.
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The Chief Super didn't know how Sherlock had been used...but wasn't Sherlock written up in the press a lot?