Subgroup presentation for image of group homomorphism

Question

In general, given a finitely presented group, it's not possible to find a presentation for an arbitrary subgroup without some other condition like finite index. I was wondering though if one was given two finitely presented groups $G$ and $H$, and a homomorphism $f:G\rightarrow H$, is there a method for finding a presentation of the subgroup $f(G)\subset H$ in terms of generators and relations of $G$ and $H$?