I see that flieder here has good points to play with authorities.
He/she did pay already the fine.
What followed was an additional violation notice for not communicating the actual driver.
A violation strictly linked to the possession of an Italian driving license (points).

I would just write them succinctly explaining the issue, enclosing the paid fine invoice, and wait for a reply.
Not an appeal, but just a follow up at the email provided.

- - - -

Due the huge amount of appeals filed against any kind of infringement, trusting in time barring, few years ago the ministry has changed the rules, effectively making this practice less alluring, with the aim of reducing any misuse.

Now it has added costs and, I can tell by experience, the two authorities in charge of assessment appeals (Govt. officer called Prefetto and small claim court) are unlikely to rule against the effectiveness of speeding equipments and the procedures of correctly use them.

And it's true, an unpaid fine, disputed over and over back and forth, in a 5 years time can easily top x10 its original value.
It happens when it lands to the collection Agency, the supremely hated Equitalia.

Now as a tourist it all depends on how tick is your skin and your willingness to invest time in it.
Having been in Australia and New Zealand 11 times as a tourist and knowing the inclination for road ambush in these two countries I learned the hard way to stick religiously to the limits and making sure to pay my fines within hours.