Process of elimination: Your program can write to the C drive. So it's not your code that is at fault.
You didn't come out and say it, but your comments in post #4 suggest that an attempt at a direct copy from the Windows GUI must have worked. So it isn't a traditional security issue, either.
If your user ID has Full Control permissions on S: and you are not doing a "Run As" (implying that Access is running as YOU, not as someone else like SYSTEM), that means it isn't a permissions issue on the S: drive. Full Control is Full Control; there are no "flavors" of that level of permissions.
Network security permissions (on the share folder) are separate from the Full Control set that you mentioned, They could equally prevent writing from the Windows GUI and from MSACCESS. But the GUI works. So it isn't likely to be NETWORK permissions on the folder either.
What is significant to me is that you can copy to the folder but can't directly create the file from Access. This might be a NETWORK FIREWALL security issue. File copying via the Windows Explorer GUI uses SMB to get to other shared folders on other systems regardless of which O/S is in play. So it isn't a general SMB protocol block. If it really IS what I begin to think it is, the file copy would ALSO fail if performed by Access because the SMB protocol isn't the problem; it is the program doing the sending.
Your problem APPEARS at first glance to be using SMB from something OTHER THAN Windows Explorer to write to a share on another server for which you have Windows Full Control over the share.
You need to talk to your site's security administrator and ask if they have put a block on SMB traffic from specific applications (such as MSACCESS.EXE). This would be at either a segment "smart" router or segment firewall that leads to that server from the network segment where your machines are located. It has to be something that is context sensitive, so a "normal" router wouldn't do this.
I had the same problem getting to one of our site's SMTP Gateway systems because it blocked programmatic transmission. Since I was using Access and the CDO library to get to that server, I got blocked. We had to get an exception posted in the smart router for that system and MSACCESS.EXE so that we wouldn't get blocked.