Thomas Kyd (1558—1594) is best known as the author of The Spanish Tragedy, a play that shares several similarities with Shakespeare's Hamlet. These similarities include a ghost demanding vengeance, a play-within-the-play used to trap the (suspected) murderer and (feigned or real) madness.
Kyd is also thought to have written a play now identified as Ur-Hamlet, which may have been an earlier version of Shakespeare's Hamlet. According to the Wikipedia article about the Ur-Hamlet
Some scholars[who?] believe that the Ur-Hamlet had influence from the German work Der bestrafte Brudermord.
The Wikipedia article about the German play mentions several scholars in the section about the relationship between that play and Hamlet but has fairly little to say about the play's relationship to the Ur-Hamlet. Volume 1 of Simon Williams's Shakespeare on the German Stage (Cambridge University Press, 2004) contains the following footnote discussing the relationship between Hamlet (especially the First Quarto of that play), the Ur-Hamlet and Der bestrafte Brudermord:
The vexed question of the relationship between Der bestrafte Brudermord and the various versions of Hamlet is discussed in detail by Reinhold Freudenstein in Der bestrafte Brudermord: Shakespeares Hamlet auf der Wanderbühne des 17. Jahrhunderts (Hamburg, 1958). He reviews the thirty-five articles on the subject written between 1857 and 1958. Four of these claim it was based solely on the first quarto, four of them on both quartos, one of them on the First Folio, seven of them on the First Folio and the Ur-Hamlet, and nineteen of them on the Ur-Hamlet alone. Some authorities even believe Der bestrafte Brudermord may be translation of the Ur-Hamlet. Freudenstein insists that whoever wrote it did not base his version on any source, but used whatever elements he felt would please the audience.
Based on the above quote, the first scholarly publication about the relationship between Der bestrafte Brudermord and the Ur-Hamlet may have been published in 1857. Is that unnamed publication the first one to claim that the German play influenced the Ur-Hamlet? Or did that publication assume the influence was in the opposite direction?