  Motivated by the decidability question for the theory of real exponentiation
and by the Transfer Conjecture for o-minimal exponential fields, we show that,
under the assumption of Schanuel's Conjecture, the prime model of real
exponentiation is embeddable into any o-minimal exponential field, where the
embedding is not necessarily elementary. This is a consequence of an
unconditional model theoretic embeddability result that we obtain by applying
K\H{o}nig's Lemma.
