Four months after the death of Hercule Poirot, his friend and associate Captain Hastings is contacted by Poirot’s solicitors and given a letter from the dead man*. When Hastings  has recovered from the shock of its contents, they ask if he will help them, for a fee, to tidy up some of Poirot’s business affairs. Hastings, at something of a loose end, agrees, and travels to the flat in Whitehaven Mansions for a meeting with Miss Felicity Lemon, Poirot’s one-time secretary.

In order to help Hastings set Poirot’s papers in order, Miss Lemon realises that she will have to explain to him her filing system, which had finally reached the state of perfection of which she had always dreamed. This explanation might take some time…

The filing system contained and cross-referenced all the information about every case that Poirot had solved – each clue, each motive, each suspect, each alibi and each murderer.

Also filed away were all of Poirot’s notes for his unpublished masterwork, ‘The Criminal Psychology‘.  Hastings decides that he will put these notes into some kind of order and get them published as a tribute to his old friend. He realises that that will also take some time, and so he decides to rent the flat while he works on it.

Miss Lemon then shows Hastings a pile of unanswered correspondence from people wishing to consult Poirot, unaware of his recent demise. Now, Miss Lemon has been out of a job for four months, and Hastings has a brain-wave: he invites her to become his own personal secretary, and she agrees.

His first instruction to Miss Lemon is to contact the landlord of the flat and enquire about a lease. His second is that she should reply to each of the letters, informing the correspondents that Poirot is dead, but that his long-time associate Captain Hastings is available should they wish to consult him instead.

As Miss Lemon types away furiously, there is a tap on the door.  It is Inspector Japp….

NOTE
* See the final chapter of Curtain, by Agatha Christie