Errett Bishop's formulation of Diaconescu's theorem

Question

The Wikipedia article on Diaconescu's theorem states that

Already in 1967, Errett Bishop posed the theorem as an exercise (Problem 2 on page 58 in Foundations of constructive analysis).

The exercise instructs the reader to

Construct a surjection which is not onto.

Definitions

Let $A$ and $B$ be sets, and $f$ a function from $A$ to $B$.

1. If there exists an operation $g$ from $B$ to $A$ such that $$f\big(g(b)\big) = b$$ for all $b$ in $B$, then $f$ is called surjective and said to be a surjection.
2. If $g$ is a function from $B$ to $A$, then $f$ is called onto and said to map $A$ onto $B$.

Question

Why is Bishop's exercise equivalent to Diaconescu's theorem?