Sorry, it's not that cut and dried. You chose the understanding you want to believe.
The following example is a silver half shekel from in the Enna hoard and other Sicilian hoards indicating that this coin was struck in Carthage for use in the Sicilian campaign of 213 - 210 BC. Experts disagree on the identity of the portrait; many identifying it as the god Melquarth, others as Hannibal or his father, Hamilcar. The elephant is clearly African.
Here are some more coins depicting Hannibal:

Coin attributed to Hannibal (as Hercules)

Coin attributed to Hannibal

Silver Half-Shekel said to represent Hannibal c.220 BC

Carthaginian shekel from the time of Hannibal (ca221-201BC)