No reason to be snarky- I'm still learning, too.
Falabellas don't really have any distinguishng characteristics, and cross breeding a mini and a falabella will just equal a miniature horse because, even as you said, falabellas did indeed originate from minis. They are simply a more 'pure' line of miniatures than you generally see, with specific lineages much like the crabbet arabian. They're still arabians but called something else because of the purity in their lines. Mixing pure and not pure irradicates the pure and leaves just another mix. Thus, this horse- whether he is partially falabella or not, is just a miniature horse. (and a cute one at that!) There is nothing except for a piece of paper than would show that he was anything but miniature because they have the same general 'look.'