homological algebra – Exercise with exact sequence in an abelian category

Suppose (in an abelian category) to have two exact sequences, $0to Axrightarrow f Bxrightarrow g Cto 0$ and $0to A’xrightarrow {f’} B’xrightarrow {g’} C’to 0$, and three arrows $a:Ato A’$, $b:Bto B’$ and $c:Cto C’$ such that the two squares that arise are commutative. I must prove that if $a$ is an isomorphism, then$$ xleftarrow b Bxrightarrow g $$ is the pullback of $g’$ and $c$. I don’t know if it’s useful, but it should be sufficient to prove the same statement with $A’=A$ and $a=1_A$; however I don’t see how, given two maps $h:Dto B’$, $k:Dto C$ such that $g’h=ck$, one could define a map from $D$ to $B$.