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?