While the first recorded mention of this sandwich was in the 1940's, we have a couple of facts that can be seen and laid out here for everyone's view:
2. Jelly can likely be traced back to the Middle East, where sugar cane grew naturally. Mixing some macerated fruit with the ground sugar cane and cooking it down, reducing it, could have produced a very simple jelly if not a fruit spread. Scientists believe that this happened before the Crusades, as it was likely Crusaders who brought the idea of jelly in to Europe. Modern jelly probably did not exist until much later, around the 16th century when the Spanish used sugar cane syrup to preserve fruit. Pectin was not extracted from apples to make jelly until the late 17th century.
3. While some could point out that South America had peanuts and the India actually had the first sugar cane, then could the two have collided at some point and created the sandwich? I guess this comes down to the bread.While the Middle East and India may have had sugar cane or sugar first, their bread has been a thin bread not made with any yeast, so it would have resembled a rolled or very skinny and flat sandwich. While the more leavened bread would have required grains and yeast to rise and would likely have originated in the Scandinavian countries, it could be noted that Spain did have a grain bread like what we are familiar with now, in America.
This being said, thanks to help with wikipedia, by looking up different histories, it could be seen that the Spanish may have invented more closely what we refer to as peanut butter and jelly. The Spanish Conquistadors brought peanuts over to Spain and if Spain already used honey and sugar by then in their fruit preserving, then the love of the peanut and jelly could have kindled. If Spain had access to honey or sugar around the 16th century and had access to peanuts or ground peanuts and bread, then they could have sliced it in two and created the first peanut butter and jelly sandwich.
Now, whether you prefer grape, strawberry or another flavor of jelly, wheat, white or another kind of bread and chunky or smooth peanut butter, that is another story.