It was not directly indicated in the letter but kind of implied; and Shulli was trying to make the uncle and the grandma testify that Johannes was the one who wrote the letter and it was his legitimate signature in it.
The Empress' late sister looks extremely identical to Shulli and she, the Empress with the red hair, wanted to test Shulli if she deserves the position as the temporary head of the Neuschwanstein territory. According to spoilers from the novel, they, the Empress and Shulli, got closer later in the story

So what exactly was Shuli trying to prove during the trial arc using the children’s uncle and grandmother? What did that flash back referring to the lavender roses and shuli’s husband have to do with the trial, right before the queen threw out the case?