You really need a proper spec, rather than the above.
It's fairly likely that this is a form-encoded HTTP POST. You need to package the XML file into a string, then encode it appropriately to make a HTTP POST. For example, that might look like something like:
xmldata=your XML file, url encoded as necessary
Assuming they are actually expecting a form-encoded POST.
Then you make the HTTP post from your server to theirs, making sure you send the appropriate headers (e.g. content-length, content-type). This can be done using fopen by creating a stream context (for instance).
Note that the above does not look like a valid XML file - because it uses the wrong type of quotes.
Check your XML file using a tool like xmllint.
Be mindful of the encoding that the XML file is using.
Mark