Update: If you are reading this discussion then please note that what others have pointed out is absolutely correct.
i.e. dependencies are preserved in both decompositions.
Actually, I was simply checking whether $F_{1}^+ \ U\ F_{2}^+ = F^{+}\ or\ not.$
But the correct approach is $(F_{1}^+ \ U\ F_{2}^+) ^{+}= F^{+}$
i.e. We take the union of F1 and F2 and then keen closure.
Thankyou @joshi_nitish, @Hemant, @Mk.