Best way to transfer about 200GB of files between two windows servers

The source server is Windows Server 2003 (a VM hosted in Xen).
Target is Windows Server 2016.

They're in different locations and the connection is roughly 30Mbit/s and they're both on the same vpn.

I need to transfer files from one to the other.

File sizes range from a few MB all the way to a few 25 GB outlook pst's.

Compressing files on target to speed things up (and have the ability to verify the copy) is out of the question (at least for the huge files), as I only have 2GB of space left in the source server.

I need something that can compress the data on the fly, transfer, and then have it uncompressed on the target server, which would speed things up greatly, and I also need to be able to verify the integrity on the files in the target server.

This is a one-time thing, as the source server will be decommissioned once I'm done.

Does anyone have suggestions?

Thanks!

Alex

Edit 2019-10-06: I didn't know a question could be down-voted, and the one downvote I got states (when hovering the mouse on the count) that no research seems to have gone into the question. On the contrary, I have spent days looking for viable alternatives to simply mapping a drive and doing a windows copy (which I also tried). Hence my question.

Edit 2019-10-06.2: I ran a few tests today:

• The large files (over 1GB amount to about 160GB).
• FTP server.Transfer uses about half the bandwidth I have available (maxes at 1.5MBytes/s without compression. Desisted on compression (mode z) because the overhead made the transfer slower. FTP would be more practical for the smaller files, as clients make the process easier.
• Justbeamit.com seems to use all my bandwidth, yielding speeds of about 3MBytes/s, which is the direction I'll probably follow with the 15 very large .pst files I have to deal with. Have to do it one by one, but for such a small number of files it's not a big deal. SHA-256 tests on source and copy of test file confirm that transfer is reliable. (Justbeamit.com allows sending multiple files but I'm hard-pressed to let it zip 160GB worth of data.) – from https://superuser.com/questions/314325/direct-transfer-of-a-file-between-two-computers-on-the-internet