for the record, I've never used or looked much into using curl. I don't know its capabilities but will try to provide some type of theory for you.

so, you obviously can't just edit a file on the web and then submit to it, that would be such a huge security risk. what you could do is, if curl allows you to anyway, save the output you're getting for the form to a variable in your script, change the "action" parameter of the <form> to whatever you're looking for, and then save the file on your own server. then, you can submit to it. this is assuming that their script allows you to POST to it from another website, though. other than that, I have no idea how you could possibly do it.