  Let $f$ be a continuous ring endomorphism of $\mathbf{Z}_p[[x]]/\mathbf{Z}_p$
of degree $p.$ We prove that if $f$ acts on the tangent space at $0$ by a
uniformizer and commutes with an automorphism of infinite order, then it is
necessarily an endomorphism of a formal group over $\mathbf{Z}_p.$ The proof
relies on finding a stable embedding of $\mathbf{Z}_p[[x]]$ in Fontaine's
crystalline period ring with the property that $f$ appears in the monoid of
endomorphisms generated by the Galois group of $\mathbf{Q}_p$ and crystalline
Frobenius. Our result verifies, over $\mathbf{Z}_p,$ the height one case of a
conjecture by Lubin.
