The Professor is a friend of Wilson's; he's also gay (as others have pointed out, in that time and place a crime) and this fact has been discovered by the Germans and turned to their advantage, probably through blackmail. Wilson has been made aware of this and of the necessity of neutralizing the Professor, a decision with which he regretfully agrees, however, since the professor is a personal friend of Wilson's, the British give him the option of helping set up but not actually participating in the murder, allowing him to "tie his shoe" at the moment of truth--(when you do that, you bend over, concentrate on what you're doing and don't see what's happening right in front of you.) "Tying his shoe" meant that Wilson was given the option of deliberately not witnessing or participating in the murder of his friend.
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