I had to do one step more before sudo-update grub, because I've got this message:
Warning: os-prober will not be executed to detect other bootable partitions. Systems on them will not be added to the GRUB boot configuration. Check GRUB_DISABLE_OS_PROBER documentation entry. Adding boot menu entry for UEFI Firmware Settings ...
the solution was add the line GRUB_DISABLE_OS_PROBER=false
after the last entry of /etc/default/grub
(sudo nano /etc/default/grub and add the line after the existing entries)