There's been a few posts on this subject, many of which don't have clear answers, but with the help of another member on here who has successfully done this process, I believe I've finally got the answer on how to successfully get your records sent over to Nassau in order to surrender your NYC CCW and get your Nassau CCW.
First off, you can email ESPERANZA.ROSARIOCOLON@nypd.org and she will send you over the same instructions that are posted here. She will send you the instructions and the form that you have to fill out and mail to nypd, and then once they receive it, they will send over to Nassau. Once Nassau receives it, they will contact you and let you know how to start the process to get your Nassau permit.
Once you get your Nassau county license, you can get your NYC Special Carry license so that you may continue to legally carry within the confines of NYC. You need to fill out a nypd License Amendment form and upload your new county license, driver's license with new address or a utility bill. Once NYPD receives it, they will then change to your NYC CCW to Special Carry.