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
Dreamweaver – (free trial only)
AndFTP (for Android)
Fire FTP (addon feature of Firefox browser)