What is the con artist's story?

Like Saki's story "The Open Window," his "Dusk" contains a story within a story. The con artist's story has been carefully worked out and rehearsed. The details are complex but the whole hard-luck tale has been condensed to relatively few words.

"Came up this afternoon, meaning to stay at the Patagonian Hotel in Berkshire Square," continued the young man; "when I got there I found it had been pulled down some weeks ago and a cinema theatre run up on the site. The taxi driver recommended me to another hotel some way off and I went there. I just sent a letter to my people, giving them the address, and then I went out to buy some soap — I'd forgotten to pack any and I hate using hotel soap. Then I strolled about a bit, had a drink at a bar and looked at the shops, and when I came to turn my steps back to the hotel I suddenly realised that I didn't remember its name or even what street it was in. There's a nice predicament for a fellow who hasn't any friends or connections in London! Of course I can wire to my people for the address, but they won't have got my letter till to-morrow; meantime I'm without any money, came out with about a shilling on me, which went in buying the soap and getting the drink, and here I am, wandering about with twopence in my pocket and nowhere to go for the night."

Without saying as much in so many words, the stranger conveys the impression that he is a member of the country gentry. He is too fastidious to be able to tolerate the kind of soap furnished in hotels. This grifter suggests that he is accustomed to traveling abroad when he says he doesn't like "hotel soap." Presumably the Patagonian, where he had originally been planning to stay, was a five-star hotel. An important detail of this story is contained in the comment,

There's a nice predicament for a fellow who hasn't any friends or connections in London!

When Gortsby finds what he believes to be the grifter's lost cake of soap, he hurries after him because he is afraid he might have lost an opportunity to make friends with a gentleman of a superior social class.

In another moment Gortsby was scudding along the dusk-shrouded path in anxious quest for a youthful figure in a light overcoat.

Gortsby himself is nothing but an office worker.

Money troubles did not press on him; had he so wished he could have strolled into the thoroughfares of light and noise, and taken his place among the jostling ranks of those who enjoyed prosperity or struggled for it.

Gortsby could be described as a member of the upper-lower class, whereas the young grifter presents the picture of a member of the upper-middle class. Some of his vocabulary suggests that he might have been to Eton and Oxford. Gortsby is anxious to catch up with this stranger in order to lend him a sovereign, return the cake of soap, and apologize for doubting him and hurting his feelings. Gortsby still hopes to become further acquainted with the young man who would almost certainly return his borrowed sovereign and invite him to have a drink or even dinner. Since the stranger knows nobody in the whole city of London, Gortsby could be of continuing service to him. They might become friends. Gortsby might even be invited to the country house for shooting and that sort of thing.
Gortsby is not acting out of compassion but has taken the bait offered by the carefully crafted words

There's a nice predicament for a fellow who hasn't any friends or connections in London!

Gortsby will be looking for his sovereign in the mail for a long time before he realizes he has been taken in. There can be no doubt that the young country gentleman knows where to send the sovereign or where to call upon Gortsby to thank him in person.

"Here is my card with my address," continued Gortsby; "any day this week will do for returning the money, and here is the soap — don't lose it again it's been a good friend to you."