How to make a live Ubuntu 18.04 USB with a persistent storage of more than 4GB

I suggest that you try mkusb. It can create a persistent live drive with a casper-rw partition almost automatically (it is an option in the graphical user interface).

• The size of the casper-rw partition is only limited by the size of the USB drive (and the size of a 'competing' usbdata partition (for exchange of data with Windows) that you may give drive space). You can select 100% (of the remaining space, when the system files are installed) for persistence and use most of the drive space for the casper-rw partition.

If you run standard Ubuntu live, you need an extra instruction to get the repository Universe. (Kubuntu, Lubuntu ... Xubuntu have the repository Universe activated automatically.)

sudo add-apt-repository universe  # only for standard Ubuntu

sudo add-apt-repository ppa:mkusb/ppa  # and press Enter
sudo apt-get update
sudo apt-get install mkusb mkusb-nox usb-pack-efi

Links

help.ubuntu.com/community/mkusb

help.ubuntu.com/community/mkusb/persistent

Quick start manual mkusb version 12 alias mkusb-dus

**Full Install to USB - BIOS/UEFI **

Full installs have a few advantages over Persistent installs, more secure, faster boots, better file management, but do not work installing Ubuntu.

If you would like your USB drive to be able to boot from multiple computers, both BIOS and UEFI:

Use mkusb to make a Live system on the Installer USB (2GB or larger).

Use mkusb to make a Persistent system on the Target USB, 16GB or larger, using default settings with ~12GB persistence, (remaining NTFS partition is used as Windows accessible data partition).

Open GParted and delete sdx4, the ISO9660 partition and expand sdx5 into the recovered space, sdx being the device name of the Target drive.

Unplug or remove HDD before proceeding further, (optional but recommended, highly recommended in UEFI mode).

Boot Installer drive, select Try.

Insert Target drive

Start Install Ubuntu...

Select Something else.

Select sdx5, (on the target drive), and click Change.

Select Use as: ext4, Format and Mount point: /.

Don't touch any other partitions (unless adding a /home partition).

Select sdx5 for boot loader installation.

Complete installation.

Cut grub.cfg from sdx5/boot/grub and paste to sdx3/boot/grub, overwriting the existing grub.cfg file.

Boot the target drive and run sudo update-grub to add all drives to boot menu.