Depends upon what you mean by "remote computer". On the same network then use standard File operations and UNC paths. This assumes the user has permissions to both servers. If you need more complex logic then simple file operations then you can also call out to a tool like robocopy.
If you need to transfer files to a machine across the Internet then that is what (S)FTP is for. .NET Framework supports FTP but .NET Core/6 no longer do. You'll need to use a third party library.
However FTP is archaic and annoying to work with. There are quite a few file transfer services available online now that have APIs to allow you to better integrate this kind of functionality. However you'll want to look for services that allow you to control what happens when you get files and not just file sharing services as they aren't sufficient here.