TL;DNR: As usual, the answer is, "it depends." In this case, it depends on whether you ever worked on this deal while you were in the state that requires a license. US courts have consistently held that a broker or agent who is not physically present in a state is not "doing business" in the state, and thus not subject to its licensing laws.
First, a point of clarification. There is no such thing as a "business brokers" license. Those states that require business brokers to have a license, require them to have a real estate license. So business brokers are subject to the same laws as real estate brokers.
Thus, in Florida, the state the OP is interested in, "real estate" is legally defined to include:
any interest or estate in land and any interest in business enterprises or business opportunities… FLA. STAT. §475.01(1)(i)
Similarly, a "real estate broker" is defined as:
a person who, for another…sells…business enterprises or business opportunities or any real property… FLA. STAT. §475.01(1)(a)
The statute goes on to say that to sell real estate, (which, in Florida, by definition includes "business enterprises") you need to have a Real Estate Broker's license.
As I said above, the basic law for selling real estate in another state is simple: If you work on a deal while you are in a state, you need a license from that state.
This rule has been consistenty applied by courts. For example, in Consul v. Solide, 802 F.2d 1143 (1986), the US Court of Appeals said, "All relevant authority suggests that licensing schemes like California's do not apply to out-of-state activities regarding in-state land." The Court goes on to point out that "courts have found real estate licensing statutes inapplicable to transactions in which brokers performed all of the regulated functions outside the state in which they were not licensed."
Of course, this general rule is subject to a host of of details on matters such as whether you need to put a choice of law provision in any contracts, and so on. You can read more about the specifics of the law covering brokers selling land in another state here.
Caveat: If the business you are selling has issued stock, then you are subject to state and federal securities law.