Well, in some eastern Churches, Pilate is venerated as a saint, the story being that he ended up converting.
It's not impossible.
Not sure about the letter itself, as I haven't studied it much.
Pilate was then like Padre Pio is today, the stuff of much legend. Catholic Encyclopedia says that "legend has been busy with his name". There are 15 different versions of whatever became of Pilate, due to his intriguiging character in the Gospels, where he seemed to have some natural virtue (having judged Our Lord to be innocent), but succuмbed to fear. Some having him meeting a bad end (ѕυιcιdє), whereas others that he converted (along with his wife Claudia) ... just like there are hundreds of "saying" falsely attributed to Padre Pio. I think there must be a reason some of the eastern Churches venerate him as a saint. They wouldn't have done so without some factual basis for it. I believe it was the Coptic and Ethiopian Churches that held that he became a Christian and died a martyr.