A.
After a place, site, structure or building has been duly designated by the Town Board as a landmark or landmark site or within an historic district, the owner(s) of said landmark or landmark site or the owner of property in an historic district shall be eligible for reimbursement of the following taxes:
B.
The owner(s) of a landmark or landmark site or the owner of property in an historic district shall be reimbursed for the proper and timely payment of only those taxes accrued after the date of formal designation of the landmark or landmark site.