This was a problem I had recently. My Ubuntu install is very customized so I wanted to copy everything and just update the files in place
- Boot using Ubuntu USB Installer
- Install Ubuntu into the new machine. Choose the barebones installation.
- Reboot into the new installation, then reboot into the USB installer again.
- Choose Try Ubuntu
- Open Gparted
- Copy source partition into the partition in the new device where Ubuntu is installed. It might be a partition within a partition, and is usually the largest one.
- Wait
- Reboot. Should boot okay now.