I'm running Debian Buster on a ThinkPad T420 which is equipped with a 250 GB SSD. Since I needed more disk space I used Clonezilla to clone my current Debian installation from the internal 250 GB SSD to a new 500 GB SSD connected via an USB to SATA adapter. Afterwards I replaced the 250 GB SSD with the 500 GB SSD and used GParted live to increase the size of the extended partition (/dev/sda2) and the LVM2 PV partition (/dev/sda5). Everything worked fine and the system is up and running again. Unfortunately, I cannot use the new space yet, because the root LVM also has to be resized:
user@debianbook:~$ lsblk
NAME MAJ:MIN RM SIZE RO TYPE MOUNTPOINT
sda 8:0 0 465,8G 0 disk
├─sda1 8:1 0 243M 0 part /boot
├─sda2 8:2 0 1K 0 part
└─sda5 8:5 0 465,5G 0 part
└─sda5_crypt 254:0 0 465,5G 0 crypt
├─user--deb--vg-root 254:1 0 204,3G 0 lvm /
└─user--deb--vg-swap_1 254:2 0 7,9G 0 lvm [SWAP]
Which steps are necessary to increase the root LVM on /dev/sda5?