This question doesn't apply only to "Jack" but to known serial killers. (of the "lust" variety if you will)
(I don't personally believe the Ripper communicated with police, although the letters are a great part of the lore)
Generally speaking it seems that most if not all communiques are dismissed by authorities unless the offender provides information nobody else could know. Multiple reasons for this and probably the sheer volume of hoaxes being the top.
Back to the thread title: Has a serial murderer ever written letters that police officials dismissed at the time and been revealed as genuine only after they were captured?
I am sure I once read about a case where one of the letters was deemed a fake, but then later found to be genuine, but can't for the life of me remember what case it was. I dont doubt somebody else will be able to help you here...
John Douglas told the police in the Green River case that the killer would not write letters. After arrest, Ridgway was like 'Didn't you guys get my letter?' Douglas also said one of the murders was a copycat because the killer had 'dressed it up' with items. We now know she was indeed a GRK victim. Douglas' profile was so diametriclly different from Ridgway that the police dismissed him as suspect. He was a suspect up to that point. Needless to say, police haven't had faith in sk profilers since the early 90s. I think the only people who still do are Ripperologists.
Didn't the BTK killer, Dennis Rader, write a letter to the authorities about the murders of the Fager family in Witchita? He claimed to be BTK, though he was disbelieved, but denied he was the killer in their case. He admired the unknown killer's work, however. Much later the letter was proved to have been written by Rader.