The compositions will both map to \$$f . h\$$.
$$\begin{array}{c|c} \text{morphism }f & F~f \\\hline \text{id}_A' & \text{id}_A \\ \text{id}_B' & \text{id}_B \\ \text{id}_C' & \text{id}_C \\ \text{id}_D' & \text{id}_D \\ f' & f \\ g' & g \\ h' & h \\ i' & i \\ f' . h' & f . h \\ g' . i' & f . h \end{array}$$