  We address the following question. For which finitely generated pro-$p$
groups the comparison map $\phi^2:H_{cont}^{2}(P,\F_p) \to H_{disc}{2}(P,\F_p)$
is an isomorphism? We prove that if $P$ is not finitely presented then $\phi^2$
is not surjective. Furthermore, if $P$ is finitely presented $\phi^2$ is an
isomorphism if and only if the comparison map $\phi_2:H^{disc}_{2}(P, \F_p) \to
H^{cont}_{2}(P, \F_p)$ of second homology groups is an isomorphism. This is the
content of Theorem A.
  The second main result of the paper is Theorem B, which gives an explicit
construction of a cochain from the kernel of $\phi^2$.
