"He's a teacher of medieval literature, the one the students hope they don't get."
-Indiana Jones and the Last Crusade
The story of the Holy Grail's journey from Jerusalem to Avalon is woven into the Arthurian legend itself! Either Joseph of Arimathea (who, in the New Testament, has Jesus buried in the tomb he had originally purchased for himself) or one of his descendants brings the Grail to Britain while evangelizing the country. The first Arthurian story with a true Holy Grail, written by Robert de Boron c. 1200, is sometimes called L'estoire dou Graal and sometimes Joseph d'Arimathie. You don't need any Old French to understand how that one works.
"Bringing our Holy Land to Europe" is not an uncommon medieval Christian way of thinking. The medieval legend of Mary Magdalene has her do penance for her sins in the Egyptian desert, then become the apostle to France.
Arthuriana is also drawing on a version of the translatio of various types of civilization, which is more like transfer than how we think of translation. It's the shift of the center of some sort of power--empire, scholarship, church--from one era's star place to the next. Thus in the translatio studii, whose name likewise speaks for itself, Babylon gives way to Greece, gives way to Rome, gives way to Paris.
Joseph and his descendants, however, are only the in-universe explanation for the Grail's journey northwest. The scandal here is that there was no preexisting "Grail at Avalon" legend. Robert de Boron did not decide that his knights would quest for a sacred relic guarded jealously by the monks of Glastonbury, the real-world location of Avalon. For all intents and purposes, Robert invented the legend of a British Holy Grail. To some extent, you could even say he invented the Holy Grail entirely.
To understand how and why Robert holds this title and why most people have never heard of him (or considered that the Holy Grail could be a 12th century invention), it's important to know that every book or other media about King Arthur is fanfiction without a canon.
The through-plot of Igraine, Merlin, Arthur, and Mordred is first laid out in writing by Geoffrey of Monmouth in the 1130s History of the Kings of Britain. But Geoffs was putting his own (extensive) twist on a whole lot of earlier literature--written and most likely oral, or at least, oral once upon a time--that he swirled together. Merlin, for example, is based on two earlier characters from two very different sets of legends.
The adventurous, chivalric, knights of the Round Table, are rooted in another 12th century series of stories, with Chretien de Troyes (which may or may not be a pseudonym) writing in the developing "romance" genre. Not in the Hallmark/Lifetime sense--you can think of these as proto-novels, while Geoffs modified the chronicle/history genre.
Chretien isn't the only writer doing so in the 12th century. Some of the lays (more fairy tale-ish, I guess you could say) of Marie de France are considered Arthurian, for example. But he is by far the most important. He's the one who really introduces Lancelot and the other major knights to Arthuriana. In our case, the most relevant one is Perceval.
So Chretien is essentially taking the Arthurian universe, and setting his stories about knights and ladies in it.
His works became wildly popular. Chretien didn't finish one of them--Perceval, and this matters--and multiple people wrote their own ending(s) that also became reasonably popular.
After 1200, Arthuriana really began to expand. Some authors, like Robert de Boron, added their own original (at least, as far as we can tell from surviving evidence) stories to the Arthurian universe. Others knit various pieces of the two strands based on Geoffs and Chretien into the fuller narrative that we think of as "the legend of King Arthur."
It wasn't even one person's work, either. Probably the earliest work to lay out everything is known today as the Vulgate Cycle (which has nothing to do with the Vulgate Bible whatsoever) or the Lancelot-Grail Cycle. It's actually five works, written by different people and covering different parts of the legend. Really!
The full Vulgate Cycle is waaay longer than our version today, and the five texts don't even always agree with each other. Whoever added on the fifth book, for example, put in a decent effort to undo a lot of the developments of the fourth. (Lancelot spends almost the entire fourth book doing penance for his third-book affair with Guinevere.)
And things kind of balloon from there. A Post-Vulgate Cycle doing more or less the same thing. Separate stories written into the universe with existing characters and new characters, like Sir Gawain and the Green Knight. Significant modifications, like Parzival. Works in all sorts of languages, including Hebrew and Icelandic.
There's no guide, and no single basis. It's a universe made entirely of fanfiction.
So, now, finally Robert de Boron and the Holy Grail.
Except first, back to Chretien.
His Perceval details the adventures of the aforementioned knight, including a visit to the castle of the figure we know as the Fisher King. During the meal, Perceval witnesses a strange, ghostly procession pass through the hall. One of the people is carrying some sort of dish that Chretien refers to as simply, "a grail." The only thing in this particular grail--it's not a proper noun--is a single Eucharist host, the wafer that medieval Christians all believed became the actual body of Christ when consecrated.
...And Perceval is the romance that Chretien never finished, and we never learn anything more about this grail. We don't even know if an explanation was part of the plan.
Okay, now Robert.
Robert picks up on Chretien's "a grail" and transforms it into the Grail. In Robert's version, it is the dish/cup that Robert used to collect Christ's blood during his burial in the tomb. The author is drawing on the Eucharist significance of the grail in Perceval.
I won't go too far into the religious history here unless you really want. So suffice to say, the late 12th/early 13th century is when the Eucharist is becoming a HUGE deal for the Church in terms of its relationship to the laity. Priests are starting to really, really stress its significance in religious culture as the body of Christ, not just something similar to a relic or a charm-leveled-up. It's also the first time the Church is starting to pay real attention to lay people at all, although it's not very good at it yet.
So even here, Robert is pulling contemporary ideas into the Arthurian universe, from art and everyday talk.
But Robert never put together a "full" Arthurian story, from Merlin and Arthur both being children of rape to Arthur's disappearance and prophesied return. He did write other Arthurian fanfic--I'm pretty sure he was the one to introduce the idea that Merlin was supposed to be the Antichrist, but Merlin's mother had a few things to say about THAT.
Robert's ideas are still pretty popular, apparently, because the authors of the five Vulgate books pick up on it. (It's not quite that straightforward, but...roll with it.) To the extent that the fourth book is in fact called "Quest for the Holy Grail.*
During the Holy Grail's journey from Robert to today, it will take on various meanings: the dish that caught Christ's blood during his burial, the cup that caught the blood he shed on the cross, the cup he used at the Last Supper. (Back to the matter of fanfic: that cup is part of a second legend, the Holy Chalice, that gets smushed into the Arthurian version.) But whatever its Christian significance or significances, the Holy Grail became an integral part of "the" Arthurian legend.
The version of the story we typically think of today, setting aside Monty Python, comes from a 15th century fanfic by Thomas Malory, Le Morte d'Arthur/Death of Arthur. Malory is, in fact, taking the title from the fifth book of the Vulgate Cycle (hence it being French). The book is a fairly radical editing-down of the through-plot-plus-romance-tradition. And then our kind of Arthur-Ether is even more secularized.
So! How the Grail ended up in England for Arthur's knights to take as the subject of the greatest quest is straightforward. Understanding why there was a Grail that ended up in Britain is a quest of its own.
And that is why, in Indiana Jones and the Last Crusade, Dr. Henry Jones, Sr. is a professor of medieval literature. The one students hope they don't get.