A is correct and seems fine to me, but then I'm from England!

We would appreciate a prompt reply. If you would appreciate a prompt reply then you would be thankful or grateful for an immediate response.

To me, none of those are correct. Who wrote that question? It's very poorly written. Shall is not the correct word to use. Firstly, it is getting to be an archaic word. Nobody here uses it any more. Possibly people in Britain still do. But more importantly shall is not used in a conditional situation such as this. 'Would' should be used, since the reply is not definite. We would appreciate your giving a reply soon. But to answer your question - appreciation is usually used for an action, or an object, not a person. So - B and C are incorrect, as the appreciation is of a person (you). We also don't say 'appreciate for...'. The only correct one is 'appreciate your giving'. But even then, 'your giving a reply soon' is very unnatural English...

Appreciate means "being grateful or thankful". So we shall ("be grateful to") you for giving a reply soon. Or (be grateful for) your giving a reply soon. I think A and C are correct. C sounds more proper.