Simplest method is to copy via normal drag and drop, provided you have halfway decent hardware copying locally on the same network and a wired connection, 1Terabyte will not take too long, maybe a few hours on a standard Gigabit connection.

There are other options as the Windows SMB network protocol can be a bit slow.

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Simplest method, use FTP to copy the files over at "line speed" - you can use filezilla in both client and server versions.

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If you are using Linux, you can also use "rsync" to copy files over to a remote machine, "Syncing" means it compares the files on source and destination and only copies the differences, this is a more efficient way to copy files. Do some research on the command to use, I usually use some variant of rsync -av /source/folder/ user@server:/destination/folder

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Windows also has a similar file syncing tool called "robocopy" (it's built in to every version of Windows since WinXP), With this you can also use something called "Multithreading" to copy lots of files at once if you have a lot of cores (be careful that the destination has a few cores as well as this can saturate a network link). Basic robocopy command (with threading) example is:"robocopy.exe c:\source \\server\destinaton /copy:DAT /xo /r:1 /w:1 /mt:4 /np /e" (syncs files, ignoring older files in destination, copying Data/Attributes/Timestamps, does not show progress - clutters screen, only tries once and waits 1 second for the retry - can always re run if lots of failures, copies all folders (even empty ones) to preserve structure, and uses 4 CPU threads to prevent big files stalling the copy) Lots more options but this should do for the basics. (using /COPYALL needs you to run in Administrator mode on terminal window due to the auditing admin rights this uses, not needed in most cases and won't work if you aren't copying NTFS to NTFS)