Step1: Login to your cPanel
Step 2: Click on the “File Manager”
Step 3: It will prompt with a pop-up menu ask for directory.
Step 4: Just go to your website files are stored and check the “Web Root” and press “Go.”
Step 5: “Show Hidden Files” box is checked
Step 6: then click on compress (selesct zip option) to cmpress the file.
Step 7: Once Copmpress done then click on download option
step 8: After that go to backup wizard and selest your database to take backup of database
Step 9: Go to new Cpanel Interface
Step 10 : go to Backup Wizard
Step 11 : Just click on restore option
Step 12: Click on MsSQLDatabase
Step 13: Choose the database compress file and upload it
And for more information
Please see the below mentioned video to move the website to new host with cpanel: