The derivation-space conjecture for components of multiplicative mapping spaces

Let $R$ be a commutative ring spectrum, let $A$ and $B$ be $R$-algebras, and let $f:A\rightarrow B$ be an $R$-algebra map. Write $F_{R\text{-alg}}(A,B)$ for the space of $R$-algebra maps and ${\bf Der}_R(A,B)$ for the derived spectrum of $R$-derivations. The derivation-space conjecture. The connected component of $f$ in $F_{R\text{-alg}}(A,B)$ is weakly equivalent to the connected component of $\Omega^\infty {\bf Der}_R(A,B)$. In particular, it is an infinite loop space. The claim would identify each component of the multiplicative mapping space with the corresponding component of an infinite loop space; the supplied text gives only evidence for it and does not state a resolution.