Help to setup up dual-boot of Xubuntu and Kali on two drives

I currently have Xubuntu installed on my laptop. It's the only OS, the laptop only has one SSD drive, uses LVM for partitions and that drive is encrypted. Laptop is using UEFI.

I'd like to add a second SSD drive to the laptop and install Kali on that new drive.

I believe the process would simply be to boot from a live USB of Kali and install it to the second hard drive following the normal install instructions.

Once that install is complete, reboot the laptop into Xubuntu on the first drive and do:

Code:

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sudo update-grub

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Then reboot into Kali on second drive via UEFI boot selection and do:

Code:

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sudo grub-install /dev/sda

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From reading on line, my understanding is that doing these steps would update Grub with both distinct Linux distros and present a menu at laptop startup to choose from.

Is that the correct steps for installing Kali on the second drive? Does the fact that the first SSD being encrypted have any considerations in dual-booting this way?

If this isn't correct, could someone point me in the right direction? I'm concerned about screwing up Grub as I'd prefer to have that appear than having to manually choose boot order via UEFI.

Thank you.