Depending on bandwidth and other variables your hosting site allows, I would probably suggest that you just:
1. Use UpdraftPlus to back up your source site (The site you are moving) then
2. Download the backups (Database, Themes, Plugins, Uploads & Others) to your workstation.
3. “IMPORT” the backups from your workstation into the destination site (The site you are migrating to.)
4. After the backups import successfully, refresh to see them if necessary them just select “Restore” and follow the instructions from there.
I am just a customer of the product so DO check out the YouTube videos, which is what I did.