It really depends on how aggressive and by book the local Secretary is in the two congregations.
First the Secretary in the Old Congregation needs to have an official notification of the move. In some places the person moving provides the name, address and telephone number of one Secretary to the other and they simply do the transfer. Some may insist a formal written request from the new Congregation to the old Congregation.
What gets sent, mainly is a letter that explains your current standing in the Congregation for example they may state that you are a regular publisher in good standing. If you have a position such as Pioneer, Elder or MS they may recommend you continue in the position. If you have your privileges limited they will state that.
In addition to the letter they will send your publisher card and the TMS counsel slip. No notes on any committee meetings will be sent. They may mention the action in the letter, but not the notes since they are sealed and kept by the old Congregation. If you are DFd, the old Congregation makes the final decision on reinstatement.
If you dont initiate the transfer and just fade, they may attempt to contact you to find where you moved. But, if they dont know where you moved or how to get in touch with you they can not send the letter until they do.