Why do you need a payment book. You know the dues are required and I assume paid them prior to 2015? Just ask for an address to send the payments to.
How did they get the incorrect address? Why did you not question the lack of communication a long time ago?
That makes no sense but I'm not familiar with Florida HOAs. Normally dues payments are sent to a management company for processing. Even sending them directly to the bank, they should be able to use your account number and address to credit the payments.
Certified mail costs more than standard First Class and is used in matters such as these to ensure a paper trail.

