Back up buddy need urgent solution to my problem

Hi

Kindly tell me is there any way to upload back up file directly to new server with out downloading it on PC. Actually i have changed hosting and new hosting didnt help me in website transfer. i didn’t know anything about transferring of websites. after learning and learning i uploaded it thorough file zilla but website was big so was giving error. new and old hosting none had the solution to my problem. at last came to back up buddy everything is okay except download portion my file is big so cant download on PC. it was taking hours on hours. i want the back up file directly on new server. now the question is if i have to download it first on computer then on server then whats the use of back up buddy? cant i do that through c panel and file zilla. plz give me direct uploading solution as my downloading on PC is pathetic slow.