R. Alexander Altmann, Moses Mendelssohn: A Biographical Study, pp. 307-309:
[There was in Prussia] a royal edict of August 28, 1703, which forbade the recital of a certain phrase, "for they bow down and prostrate themselves before what is vain and futile and pray to a god who cannot help," in the `Alenu prayer at the conclusion of each service. A Jewish convert to Christianity had testified that this particular phrase was meant as a slur against Jesus. To ensure the omission of this sentence from the prayer, the edict demanded that the text be recited aloud by the cantor and that the services be inspected by government-appointed Christian supervisors familiar with the Hebrew language...
This utterly ludicrous edict had actually been observed by the Jewish communities, so as to avoid giving any imagined offense, but the duty of supervising the services was no longer taken seriously by local authorities except in the city of Koenigsberg... Offended, [the Koenigsberg supervisor, named David Kypke,] lodged a complaint with the Royal Ministry of State on April 5, 1777, airing not only his personal "grievance" but also reporting that the `Alenu prayer was being recited in a sort of "muttering," rather than aloud...
In self-defense the community submitted a testimonial written (at its request) by [Moses] Mendelssohn a few weeks before his departure for Koenigsberg [in the summer of 1777, on a business trip]. It was entitled "Thoughts on Jewish Prayers, Especially on the `Alenu Prayer" and did not bear his signature... "The prayer `Alenu," Mendelssohn pointed out, "is one of the oldest prayers of our nation. It was originally instituted only for New Years's Day, as a solemn introduction to the homage paid to the Supreme Lawgiver and Judge of the World. Because of its important and sublime [erhabenen] content it has been adopted as the daily concluding prayer. It can be shown irrefutably, on a number of grounds, that only the heathens and their idolatrous worship are referred to in it, and not, as some enemies and slanderers of the Jewish nation falsely contend, the Christians, who like ourselves worship the King of Kings, the Holy One, blessed be He; that, moreover, no kabbalistic allusions to their [the Christians'] Messiah are found in it." The last remark was directed against the allegation that the numerical value of the word va-rik ("and futile") alluded to Yeshu (Jesus).
Mendelssohn then undertook to prove that this prayer had originated in pre-Christian times and thus could contain no anti-Christian passages. Indeed, some authorities had attributed its authorship to a figure of such remote antiquity as Moses' disciple Joshua the son of Nun. Yet this much was certain, that the prayer must have existed at least at the time of the Second Temple. For had it been composed later one should find there some expression of hope in the rebuilding of the Temple and the restoration of the Jewish state. The text had remained unaltered, and the fact that Jews in Muslim lands recited it in exactly the same way as Jews recited it in Christian lands was a clear indication that no anti-Christian reference was intended...
On September 2, 1777, a strong memorandum opposing Kypke's rejoinder was submitted, and in the following year a petition addressed to the king finally achieved the termination of the undignified practice.