What should we do to cover the shortfall in the amount of zakat paid to the state, which results in the amount paid being less than what is legally due, in order to avoid sin?

It is not permissible to delay the Zakat (definition) from its due time, which is upon the completion of a full year, because Zakat is obligatory immediately, according to the preponderant opinion, unless delaying it would result in harm, such as being forced to pay Zakat twice.

One-quarter of one-tenth (2.5%) of the wealth must be given as Zakat if a full year has passed over it and it reaches the Nisab (definition). The Nisab for Zakat is estimated at the equivalent of 85 grams of gold or 595 grams of silver. The rise or fall in gold prices does not affect the amount of Zakat that must be paid, as long as the wealth reaches the Nisab. This specific amount (2.5%) does not increase or decrease with the rise or fall in the dollar exchange rate.