Genrally, uploading of files through File Manager in the cPanel is quite easy. However, if you are transferring large files and folders, it is recommended that you upload them via FTP client. You may download free FTP clients of some that are most commonly used by accessing the their respective website on internet.
Free FTP clients
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Filezilla
Cyberduck
Cyberduck Mac
Dreamweaver – (free trial only)
WinScp
Core FTP
Smart FTP
Coffee cup
AndFTP (for Android)
Fire FTP (addon feature of Firefox browser)
FlashFXP