A certain merchant had three sons; the eldest was named Sálih, the second Selim, and the youngest Judar.
So opens "The Story of Judar," from Volume One of Evening Tales for the Winter. It's the story of a young man who gains some magic artifacts from a Maghrebi magician, and uses them to make his way in the world. In many ways, it's a tale quite similar to the more famous "Aladdin."
A little websearching easily revealed that this story is from The Thousand and One Nights; search for it and up pops the version from Richard Burton's famous translation, from the 1880's. He titled it "Judar and his Brethren".
But of course, the version from Evening Tales can't be Burton's, since Evening Tales Volume One was originally published in 1833 (as Volume One of Tales of Terror). Looking further back, the only other English version I could find of this story was from a translation by Edward William Lane, called "The Story of Joudar", first published sometime in the period 1838-1840 -- so also not early enough.
After further reading, I found an article by folklorist (and entomologist) William Forsell Kirby, called Contributions to the Bibliography of the Thousand and One Nights, and Their Imitations, with a Table Showing the Contents of the Principal Editions and Translations of the Nights. It's included as Appendix II of Volume 10 of Burton's The Book of The Thousand Nights and A Night. In the section "Von Hammer's MS., and the Translations Derived From It," Kirby discusses the manuscript associated with German orientalist Joseph von Hammer.
Von Hammer translated some of the as-yet unpublished tales from the manuscript into French, and later had (some? all?) of the tales translated into German by August Ernst Zinserling. This German work was published in 1824. A selection of the tales were translated into English by one Rev. George Lamb, and published as New Arabian Nights' Entertaiments, three volumes, in 1826.
It's not clear whether Lamb translated directly from the Arabic manuscript or from Zinserling's German translation. I suspect the latter. But the important part is: Lamb's work was published before 1833! Eureka!!!
Sure enough, "The Story of Judar" as reprinted in Tales of Terror and later Evening Tales for Winter can be found in Volume One of Lamb's translation.
I believe this is the first appearance of the Judar story in English, as all other English translations of The Thousand and One Nights that I could find are based on an 18th century French translation by Antoine Galland, which does not appear to have the Judar tale.
Case closed!
Incidentally, Kirby also mentions a story called "Joodar of Cairo and Mahmood of Tunis", from Gustav Weil's translation of 1001 Nights into German (1837-41). It's the same basic story, but with vastly different plot elements and narrative. Weil claims to have taken it "from a MS. in the Ducal Library at Gotha" [Kirby, Contributions...]. Kirby translated the story and included it in his 1883 collection The New Arabian Nights: Select Tales Not Included by Galland or Lane.