The well-ordering principle implies Zorn's Lemma

Question

I have read and understood proofs for each implication between $AC$, $ZL$, $WO$ except this one. These proofs need about 10 lines each. Can someone share a neat, hopefully short, proof for $WO\implies ZL$?

(obviously not using $AC$ explicitly)

(I already know this one)

Answer 1

Pedersen's book Analysis Now has a proof of their equivalence without using transfinite induction: Google books (Theorem 1.1.6).

Also note that the proof of $WO\implies AC$ is two lines long, so perhaps it is easier to prove $WO\implies AC\implies ZL$.