There will probably not be a specific year when the word converted, and there will most likely be a good few years/decades of crossover as the former word sank out of common usage. I'm watching a video where somebody is imitating the dialect of a late 1600s "Witch Finder General" and he uses "Jesu". Maybe this is historically, inaccurate, I don't know.
The English words Jesus and Jesu reflect forms of the same word in Latin and Greek. In these two languages, the grammatical function of a word is conveyed not only through word-order, but also through changes to the word's form itself. In Latin, Jesus was the form of the word when it was the subject of a sentence, while Iesu was the form in many other situations, such as the object of certain prepositions (it is a weird fourth declension word). Greek follows this in its own way, with Ιησους (Iesous) being the subject and other forms like Ιησου (Iesou) filling out the other cases. This Greek word, which is probably the source of the Latin word, is also the Greek rendering of the biblical Joshua, since both the words Jesus and Joshua are related in Hebrew (I don't know Hebrew though, so I unfortunately can't provide more info on that relation).
Because of the coexisting forms of the word in Latin and Greek, when some of the first translators of the gospel into Germanic languages had to translate Jesus, they sometimes used something like the modern form Jesus, and sometimes the form based on the Latin Iesu, or Jesu. The Heliand, a gospel harmony written in Saxon in the ninth century CE, alternates freely between Hiesu and Jesus, while Wycliff's late 14th century translation of the Gospel into English likewise alternates between Jhesus and Jhesu. At this time, Jesus and Jhesu were likely understood as variations of the same word, similar perhaps to the variation between flavor and flavour or between purposeful and purposive. This alternation is very infrequently maintained in later English sources, with the dominant form becoming Jesus at the beginning of early modern english in the sixteenth and seventeenth centuries. As for why Jesus and not Jesu is maintained in modern English, this probably is because Jesus is the nominative (subject form) of the word, which is often (though not always) the borrowed form of the word when the speaker is fluent in both languages. However, the chances of an English speaker using the form Jesu and not Jesus was influenced by their education levels, since them knowing Jesu as a form in Latin increased their likelihood of using it