Hi Ashley,
ok - the short answer is that the web server supports HTTP. With HTTP it is possible to send a POST which contains data. There are a few standard ways of formatting that data which they can use.
So the short answer is yes, they can send you data which you can process and save. The longer answer is that they need to send it, and then you can inspect it, see what the format is, and get more advice about what to do with it when it arrives.
If they want the "generic" answer then the "correct" way for them to do it is to POST the file as a file upload to a web form. they'll either know how to do that, or not - but I guess you'd need more information for us to be more specific.
but the short answer to them is "yes".
cheers
Bruce