Restore from copy of SQL Server backup file produces invalid data error
Since the local copy of the backup file is validated successfully via RESTORE VERIFYONLY, the most likely cause of the issue is corruption of the target file while it is being copied over the network.  

You can determine if the two copies of the backup file are binary-identical with the command-line utility fc:

fc /b C:\some\local\path\file1.bak \\server\share\path\file2.bak


Alternately, you could generate a cryptographic hash of each file, and see if the hashes are identical.  Microsoft offers a command-line tool for that purpose at https://www.microsoft.com/en-us/download/details.aspx?id=11533

If both files are binary-identical, the restore should complete without error.