A move has two parts. The first is the files. The second is the database. They need to belong to the same day. If the copy from the old firm is missing a part, the site on the new account drops pictures or pages.
When the address changes
Changing the nameserver before the site opens on the new account sends visitors to an empty account. Install the files and the database first, try the page on its own address, then turn the nameserver. If mail is a separate MX line, check that in the same window.
The panel
On a Linux account the install is in cPanel. On a Windows account it is in Plesk. The Linux and Windows cards state that split. When the move is done, let a backup be the first day of the new copy.