What reasons did Holmes give to prove that Barker was in collaboration with Mrs. Douglas?

From the text:

“How do I know that they are lying? Because it is a clumsy fabrication which simply could not be true. Consider! According to the story given to us, the assassin had less than a minute after the murder had been committed to take that ring, which was under another ring, from the dead man’s finger, to replace the other ring—a thing which he would surely never have done—and to put that singular card beside his victim. I say that this was obviously impossible."