Suppose Magma has computed homomorphism $h$ between function fields $F1 \to F2$. Then we have an induced homomorphism $h$ on the divisor group. Now my question is that if there's a better way to compute this homomorphism for $D2 := h(D1)$ than this way which is basically computing the image of the two generators of each place and is very slow.

Ps, Ds := Support(D1);
D2 := Divisor(F2!1);

for i := 1 to #Ps do
  g1,g2 := TwoGenerators(Ps[i]);

  G1 := h(g1);
  G2 := h(g2);

  D2 := D2 + Ds[i]*ZeroDivisor(GCD(Divisor(G1), Divisor(G2)) );

end for; 

Thank you very much indeed!