Theorem If there exists at least one pointfree funcoid from a poset $\mathfrak{A}$ to a poset $\mathfrak{B}$ then either both posets have least element or none of them.
Conjecture If there exists at least one pointfree funcoid from a poset $\mathfrak{A}$ to a poset $\mathfrak{B}$, then either both or none of these two posets are join-semilattices.