In the film, a love letter that Oliver wrote to his wife, who had abandoned him and started a new life in Paris, turns up in the Dead Letter Office. But Shane sees it before he does. Before she decides what to do with it -- but after she finds the address and labels the letter -- Norman unsuspectingly sends it out with express delivery.
When Oliver's wife arrives, she unknowingly shakes things up in a way that eventually leads to new beginnings for both Shane and Oliver and Rita and Norman. Her arrival also reveals more about Oliver, Shane and Rita.
Regarding Rita, seeing Shane's fearful reaction to Oliver's reunion with his wife strikes a chord with her. In trying to explain to Norman why Shane is so upset that she's quitting the department, she's moved to let down her guard and finally tell him how she feels. When Norman reveals that he feels the same, it's one of the most heartfelt moments and milestones in the series of films.
As for Shane, the arrival intensifies the feelings she's had for Oliver. It also reveals her insecurities. Knowing how rigid and how loyal Oliver is, she believes that he'll get back together with his wife.
When Oliver finally bends and accepts that his (practically non-existent) marriage is over, he surprises Shane in the most perfect way that remains so true to his character. When she goes home -- carrying her office belongings in a box -- Oliver is on her porch, putting together a porch swing that he bought her for her birthday, because she casually mentioned a happy childhood memory of one. It's such a thoughtful, caring gesture. But it's much more than that. He responds to her final question of what he did when he realized his marriage was over by confidently saying "I went out and bought a porch swing." Removing the band from his finger is his way of ending the relationship, but buying the porch swing is his way of beginning a new one.
So, Oliver's wife unexpectedly brings the promise of love for Shane and Oliver and Rita and Norman. And the sub-plot about the DLO mission to deliver divorce papers to a couple who aren't divorced and shouldn't end their marriage also has a great, happy twist, and it blends perfectly with the misunderstandings that can result from leaving things unsaid.
Mission #3: If there's a bad habit or a bad relationship that just ended, find a nice symbolic way of setting off in a new, positive direction.