In my experience, the only way to improve on systems like good old-fashioned email and FTP is to send multiple parts of the file in parallel, some people believe in you four quarters, I suspect that there is a lot to be said for two halves. This parallelism thrashes the TCP connections so that any idle time is soaked up properly and optimal efficiency is achieved even over a very long link. There are file transfer apps that do exactly this, and it might well be worth looking into a specialist file transfer app to be run at both ends if you need to do this a lot.
If the file is not to large to email, I'm assuming it is, then sending an email is good as the first step in the chain, uploading it to your outgoing mail send server is usually very fast as hopefully it should be really close to you on the Internet. But as I said, I assume email is a no-go.
Obviously if you can use compression then do so.
But a specialist app at both ends is going to be your best bet.
