How does a Zakat payer extract the Zakat from his wealth that reached the minimum threshold (nisab) in previous years, but for which he did not pay Zakat, and he cannot determine whether or not a full year (hawl) has passed on the amount?

The conditions for Zakat to be obligatory are complete ownership, reaching the nisab (minimum threshold), and the completion of a full hawl (lunar year). If a Muslim is not certain about the completion of a full year on his wealth, then Zakat is not obligatory upon him, because the default is the exoneration of one's liability and the absence of obligation until the contrary is proven. This is unless the Muslim is certain that it is obligatory upon him. However, if he were to pay it as a precaution, he would be doing a good deed.