Hi
I'm not clear with this statement for Server A: "The button to submit or send the data to Server B is on a php page." Do you mean that the server A is already has a page to submit its data to server B and now you need a desktop based software to submit it? If it is then just ignore my bid BUT if it is not, then, if your server (server A) installed with PHP and curl lib then you can submit the data within to server B and even it can be performed automatically, ie, by using cronjob.
BTW, it's good if you also inform the URL for that submission page for review (if it's confidential maybe you can attach the source code of that submission page, ie, right-click then click 'View Page Source', modify it a bit to exclude any domain, save and attach the file in here, this way coders can review whether the submission process is secured by obfuscated JS or such).
Regards,
Ibnu